Chapter 3
The ASVAB’s Mathematics Knowledge subtest is a big deal. It forms a large part of your AFQT score, so you need to do well on it to pass muster. This subtest covers a big range of mathematical concepts, including arithmetic, algebra, and geometry, so it’s a good idea to dust off the corners of your brain where you stashed all this knowledge during high school. You’re going to find questions that include fractions, square roots, inequalities, factoring, graphing, and much more on the test. You’ll have 20 minutes to answer 16 Mathematics Knowledge questions on the computerized ASVAB or 24 minutes to answer 25 questions on the paper version. Calculators are not allowed.
The Mathematics Knowledge subtest includes the following:
When you work on the Mathematics Knowledge questions, keep these tips in mind:
501. Solve:
(A)
(B)
(C)
(D)
502. Solve:
(A)
(B)
(C)
(D)
503. Solve:
(A)
(B)
(C)
(D)
504. Simplify:
(A)
(B)
(C)
(D)
505. Reduce to lowest terms:
(A)
(B)
(C)
(D)
506. Simplify:
(A)
(B)
(C)
(D)
507. Solve:
(A) 2
(B) 3
(C) 5
(D) 6
508. Which fractions are not equivalent?
(A)
(B)
(C)
(D)
509. Solve:
(A)
(B)
(C)
(D)
510. Simplify:
(A)
(B)
(C)
(D)
511. Find 25 percent of 200.
(A) 50
(B) 25
(C) 15
(D) 12.5
512. 250 is 40% of what number?
(A) 650
(B) 625
(C) 6,250
(D) 6,500
513. 8 is what percent of 20?
(A) 35
(B) 16
(C) 20
(D) 40
514. 15 is what percent of 375?
(A) 45
(B) 5
(C) 6
(D) 4
515. 450 is 75% of what number?
(A) 650
(B) 550
(C) 600
(D) 675
516. What is 33% of 120?
(A) 39
(B) 40.6
(C) 39.6
(D) 38.9
517. What is 55% of 150?
(A) 75
(B) 83.5
(C) 80
(D) 82.5
518. Find 8.6% of 310.
(A) 26.66
(B) 25.8
(C) 25.68
(D) 28.56
519. What percent of 56 is 14?
(A) 30
(B) 28
(C) 25
(D) 22.5
520. Find 12.5% of 989. Convert the answer into a fraction.
(A) 123.375
(B)
(C)
(D) 865.375
521. Express the ratio of ducks to geese: There are 16 ducks and 9 geese in a park.
(A)
(B)
(C)
(D) Both B and C
522. Express the ratio of women to men as a fraction and simplify: There are 15 women and 20 men in the group.
(A)
(B)
(C)
(D)
523. The ratio of a to b to c to d to e is 5 to 4 to 3 to 2 to 1. If , what is the value of c?
(A) 24
(B) 36
(C) 63
(D) 61
524. There are 27 males and 38 females in Group A, and there are 42 females and 26 males in Group B. Express these relationships as a pair of ratios of males to females.
(A)
(B)
(C)
(D)
525. Use a height-to-width ratio to express the fact that a horse is 7 feet, 6 inches tall and 10 feet long.
(A)
(B)
(C)
(D)
526. Solve for if and :
(A) 1,200
(B) 10,500
(C) 1,500
(D) Not enough information provided
527. Convert 297.85 centimeters to feet.
(A) 10 feet
(B) 9 feet
(C) 8 feet
(D) 11 feet
528. Convert 12.8 meters to centimeters.
(A) 12,800 cm
(B) 1,280 cm
(C) 1,300 cm
(D) 1,250 cm
529. One of 20 dogs at the shelter has three legs, two ears, and one tail. Express the ratio of dogs that have three legs to the remaining dogs as a fraction.
(A)
(B)
(C)
(D)
530. The ratio of 1.5 to 32 equals the ratio of to x. Solve for x.
(A) 0.4
(B) 0.45
(C) 0.39
(D) 0.43
531. Express 7,000 in scientific notation.
(A)
(B)
(C)
(D)
532. Express 0.59784 in scientific notation.
(A)
(B)
(C)
(D)
533. Express 6,000,000 in scientific notation.
(A)
(B)
(C)
(D)
534. Multiply and .
(A)
(B)
(C)
(D)
535. What number does represent?
(A) 854,345
(B) 8,543,450
(C) 0.0854345
(D) 0.854345
536. Solve:
(A) 9
(B) 6
(C) 7
(D) 8
537. Simplify:
(A)
(B)
(C)
(D)
538. Solve when
(A)
(B) 25
(C) 1.5
(D) 15
539. Simplify:
(A)
(B)
(C)
(D)
540. Solve:
(A) 114
(B) 7
(C) 12
(D) 8
541. Solve for a:
(A) 3
(B) 4
(C) 5
(D) 6
542. Solve for x:
(A) 4
(B) 3
(C) –1
(D) 12
543. Solve for x:
(A) 35
(B) –35
(C) 29
(D) –29
544. Solve for x:
(A) 3
(B) 14
(C) 21
(D) 12
545. Solve for a:
(A)
(B)
(C)
(D) Not enough data
546. What is in slope-intercept form?
(A)
(B)
(C)
(D)
547. Solve for x:
(A) 5
(B) 17
(C) 6
(D) 8
548. Convert into a mathematical expression:
The fourth root of 239 equals the log with respect to the base a of the product of x and y.
(A)
(B)
(C)
(D)
549. Solve for x:
(A) –8
(B) 4
(C) –9
(D) 9
550. Solve for y:
(A) 14
(B) 13
(C) –14
(D) 17
551. Solve for x:
(A) 3
(B) –2
(C) –3
(D) 4
552. Solve for x:
(A) 9
(B) 8
(C) 8.5
(D) 11
553. Solve for x:
(A) 4
(B) 6
(C) –6
(D) 22
554. Simplify:
(A)
(B)
(C)
(D)
555. Express in standard form:
(A)
(B)
(C)
(D)
556. Simplify:
(A)
(B)
(C)
(D)
557. Solve for x:
(A) 294
(B) 295
(C) 290
(D) 6
558. Rewrite in slope-intercept form:
(A)
(B)
(C)
(D)
559. Solve:
(A)
(B)
(C)
(D)
560. Factor:
(A)
(B)
(C)
(D)
561. Solve for x:
(A) –22
(B) 23
(C) –23
(D) –24
562. Factor:
(A)
(B)
(C)
(D)
563. Simplify:
(A)
(B)
(C)
(D)
564. Solve:
(A)
(B)
(C)
(D)
565. Identify:
(A)
(B)
(C)
(D)
566. Solve for x:
(A) 24
(B) 17
(C) –17
(D) –19
567. Find the equation for a straight line with a slope of 4 that passes through the point .
(A)
(B)
(C)
(D)
568. Simplify:
(A)
(B)
(C)
(D)
569. If and , solve:
(A) 100
(B) 110
(C) 120
(D) 95
570. Solve for x:
(A) 11
(B) 9
(C) 18
(D) 6
571. Reduce to the lowest terms:
(A)
(B)
(C)
(D)
572.
(A)
(B)
(C)
(D)
573. Solve for x:
(A) 4y
(B) 6y
(C) 4
(D) 5
574. Solve for x:
(A)
(B)
(C)
(D)
575. Which of the following is true if ?
(A)
(B)
(C)
(D) All of the above
576. Solve for a:
(A) 4
(B) 3
(C) 2
(D) –2
577. Simplify:
(A)
(B)
(C)
(D)
578. Solve:
(A)
(B)
(C)
(D)
579. If and solve for z:
(A) –1
(B) 0
(C) 1
(D) 2
580. Solve for x:
(A) 6
(B) 6 or –6
(C) 36 or –36
(D) 36
581. Solve for c:
(A) 30
(B) 3
(C) –3
(D) 60
582. Factor:
(A)
(B)
(C)
(D)
583. Solve:
(A)
(B)
(C)
(D) 2
584. Solve:
(A)
(B)
(C)
(D)
585.
(A)
(B)
(C)
(D)
586. Solve for x:
(A) 3
(B) 2
(C)
(D)
587. If and , then
(A)
(B)
(C) both A and B are correct.
(D) none of the above.
588. Solve for x:
(A) 9
(B) –9
(C) 11
(D) 12
589. Solve the system:
(A)
(B)
(C)
(D)
590. Solve for y:
(A) 7
(B) 6
(C) 10
(D) 9
591. Solve:
(A) 4
(B) 3
(C) –4
(D) 7
592. Find the equation of the line that passes through and .
(A)
(B)
(C)
(D)
593. Given in the complex plane, which of the following is not true?
(A)
(B)
(C)
(D)
594. Simplify:
(A)
(B)
(C)
(D)
595. Find the equation for a line with a slope of 50 and a y-intercept of 32.
(A)
(B)
(C)
(D)
596. Choose the appropriate graph for .
(A)
(B)
(C)
(D)
597. If and , then
(A) 30
(B) –420
(C) 420
(D) –30
598. Solve for y if , , and :
(A) 58
(B) 57
(C) 51
(D) 60
599. Solve:
(A)
(B)
(C)
(D)
600. Identify the group of prime numbers.
(A) 2, 3, 5
(B) 7, 9, 11
(C) 2, 4, 6
(D) 6, 7, 9
601. Solve for x:
(A) 5
(B) 4
(C) 0.5
(D) 2
602. What is the greatest common factor of 10 and 100?
(A) 10
(B) 1
(C) 100
(D) 50
603. Solve for p:
(A) 2
(B) 3
(C) –5
(D) 5
604. If , solve for y:
(A) 100
(B) –60
(C) 60
(D) 160
605. Solve for x:
(A) 0
(B) –1
(C) –2
(D) 1
606. Solve for a:
(A) –2
(B) 3
(C) 2
(D) 1
607. Solve for x:
(A) 4
(B) 1
(C) 3
(D) All of the above
608. Solve:
(A) 1
(B) –1
(C) 0
(D) 6
609. Simplify:
(A)
(B)
(C)
(D)
610. Solve for x:
(A) 2
(B) 2x
(C)
(D) 4
611. Simplify:
(A)
(B)
(C)
(D)
612. Solve for x:
(A)
(B) 1
(C)
(D)
613. Solve:
(A)
(B)
(C)
(D)
614. Solve for x:
(A) 12
(B) 9
(C) 8
(D) 6
615. Simplify:
(A)
(B)
(C)
(D)
616. Simplify:
(A)
(B)
(C)
(D)
617. If , , and , solve for x:
(A)
(B)
(C)
(D)
618. Find the equation for a line with a slope of 4 when and .
(A)
(B)
(C)
(D)
619. Find the equation of the line that passes through the points and .
(A)
(B)
(C)
(D)
620. Factor:
(A)
(B)
(C)
(D)
621. Solve for x:
(A)
(B)
(C) Both A and B are correct.
(D) Neither A nor B is correct.
622. Solve for x:
(A)
(B)
(C)
(D)
623. Factor:
(A)
(B)
(C)
(D)
624. Find y:
(A)
(B)
(C)
(D)
625. Solve for x:
(A)
(B)
(C)
(D)
626. Solve for x:
(A) 36
(B) 6
(C) 8
(D) 16
627. Solve for x:
(A)
(B) 2
(C)
(D)
628. Solve for x when and .
(A)
(B)
(C)
(D)
629. Express x as greater than or equal to 3 in interval notation.
(A)
(B)
(C)
(D)
630. Solve for b:
(A) 7
(B)
(C) 7.5
(D) 4
631. Solve for x:
(A)
(B) 3
(C) 2
(D) 5
632. If , find 6x.
(A) 6
(B) 36
(C) 2
(D) 24
633. Simplify:
(A)
(B)
(C)
(D)
634. Simplify:
(A)
(B)
(C)
(D)
635. Solve for x:
(A)
(B)
(C) 3
(D) 6
636. Solve for x:
(A) 2
(B) 1
(C) 3
(D) 0
637. Solve for c:
(A) 3.5
(B) 3
(C) 2.5
(D) 2
638. Simplify:
(A)
(B)
(C)
(D)
639. Express a quantity with a coefficient of 3, a base of x, and an exponent of 5.
(A)
(B)
(C)
(D)
640. Solve for a if :
(A) 3
(B) 2
(C) 4
(D) 6
641. Solve for x:
(A)
(B)
(C)
(D)
642. Express as a quadratic equation:
(A)
(B)
(C)
(D)
643. Solve for x:
(A)
(B)
(C)
(D)
644. Solve for x by factoring:
(A)
(B)
(C)
(D)
645. Solve for x:
(A)
(B)
(C)
(D)
646. Solve for x:
(A)
(B)
(C)
(D) Not enough data
647. Solve:
(A)
(B)
(C)
(D)
648. Solve:
(A)
(B)
(C)
(D)
649. Solve for x:
(A)
(B)
(C)
(D)
650. Solve:
(A)
(B)
(C)
(D)
651. According to the figure, the intersection of line a is a
(A) parallel line.
(B) right angle.
(C) transversal.
(D) complementary angle.
652. Find the perimeter of the right triangle:
(A) 35 cm
(B) 36 cm
(C) 21 cm
(D) 15 cm
653. In the figure below, which angles are complementary?
(A)
(B)
(C)
(D)
654. Find the area:
(A) 56.25 m3
(B) 56.75 m2
(C) 56.5 m2
(D) 56.25 m2
655. According to the figure, the angles formed by ray DB intersecting are
(A) supplementary
(B) right
(C) complementary
(D) parallel
656. The polygon depicted here is a/an _______________ polygon.
(A) hexagonal
(B) convex
(C) perpendicular
(D) equilateral
657. Find the area:
(A) 72 sq. ft
(B) 60 sq. ft
(C) 18 sq. ft
(D) None of the above
658. What is the formula to find the volume of a cube?
(A)
(B)
(C)
(D)
659. Identify the Pythagorean theorem.
(A)
(B)
(C)
(D)
660. Find the length of b:
(A) 24 cm
(B) 12 cm
(C) 6 cm
(D) 33 cm
661. What is the measure of angle x if L1 and L2 are parallel lines?
(A) 30°
(B) –40°
(C) 40°
(D) 50°
662. Find the area of sector c:
(A) 30.3 ft2
(B) 50.5 ft2
(C) 51 ft2
(D) 50.6 ft2
663. Find the area of this square:
(A) 125 sq. in.
(B) 25 sq. in.
(C) 10 sq. in.
(D) 15 sq. in.
664. Find the measure of the interior angle x:
(A) 206°
(B) 16°
(C) 26°
(D) 36°
665. Find angle b:
(A) 120°
(B) 125°
(C) 104°
(D) 130°
666. Find the perimeter of this square:
(A) 16 ft
(B)
(C) 12 ft
(D) 8 ft
667. Find the surface area:
(A) 48 square yards
(B) 72 square yards
(C) 90 square yards
(D) 96 square yards
668. Find the measure of ∠C:
(A) 106°
(B) 16°
(C) 36°
(D) 30°
669. Which of the following statements is true of a line?
(A) It has only one dimension.
(B) It stops at two points.
(C) It has a finite length.
(D) It has width.
670. Find the total area:
(A) 1,050 ft2
(B) 176 ft2
(C) 352 ft2
(D) 1,100 ft2
671. Find the perimeter:
(A) 88 ft
(B) 161 ft
(C) 145 ft
(D) 146 ft
672. Find the area of the polygon if the apothem a is 10:
(A) 1,100 mm2
(B) 1,000 mm2
(C) 1,050 mm2
(D) 350 mm2
673. Find x:
(A) 10
(B) 5
(C) 4
(D) 8
674. Find the measure of :
(A) 120°
(B) 60°
(C) 180°
(D) 90°
675. Find the measure of :
(A) 35°
(B) 45°
(C) 55°
(D) 40°
676. Find x, y, and z:
(A)
(B)
(C)
(D)
677. Find y:
(A) 72°
(B) 70°
(C) 64°
(D) 80°
678. Label angle a:
(A)
(B)
(C)
(D)
679. Identify the type of angle depicted:
(A) Obtuse
(B) Straight
(C) Acute
(D) Right
680. Find the perimeter:
(A) 60 ft
(B) 100 ft
(C) 37.5 ft
(D) 75 ft
681. Find the measure of in :
(A) 70°
(B) 78°
(C) 64°
(D) 112°
682. Find x:
(A) 220°
(B) 230°
(C) 50°
(D) 170°
683. Identify the complementary angles:
(A)
(B)
(C)
(D)
684. Find the area:
(A) 165 sq. in.
(B) 150 sq. in.
(C) 330 sq. in.
(D) 68 sq. in.
685. Find the area:
(A)
(B)
(C)
(D)
686. The formula for finding the radius of a circle is
(A)
(B)
(C)
(D)
687. Find the area of the circle:
(A) 28.26 in.2
(B) 30 in.2
(C) 25.8 in.2
(D) 24 in.2
688. Find the radius of the circle:
(A)
(B)
(C)
(D)
689. Identify the standard formula to find the perimeter of a rectangle:
(A)
(B)
(C)
(D)
690. Find the area of the circle:
(A) 75 in.2
(B) 78.5 in.2
(C) 75.8 in.2
(D) 78 in.2
691. Find the radius:
(A) 79 cm
(B) 52.7 cm
(C) 49.6 cm
(D) 78 cm
692. Find the circumference of the circle:
(A) 58.8 meters
(B) 60 meters
(C) 62 meters
(D) 62.8 meters
693. Find the perimeter:
(A) 47.5 cm
(B) 49 cm
(C) 41 cm
(D) 56 cm
694. Find the circumference of the circle:
(A)
(B)
(C)
(D)
695. Find the radius of the circle:
(A)
(B)
(C)
(D)
696. Find the perimeter:
(A) 17.4 m
(B) 14.5 m
(C) 20.3 m
(D) 23.2 m
697. Find the volume of the cube:
(A) 72 cubic inches
(B) 9 cubic inches
(C) 27 cubic inches
(D) 81 cubic inches
698. Find the area:
(A) 262 cm2
(B) 245 cm2
(C) 62 cm2
(D) 240 cm2
699. Find the volume of the cube:
(A) 3,375 cubic feet
(B) 3,300 cubic feet
(C) 2,500 cubic feet
(D) 3,500 cubic feet
700. Find the volume of the right square pyramid:
(A) 450 cm3
(B) 500 cm3
(C) 1,500 cm3
(D) 150 cm3
701. Find the volume:
(A) 960 mm3
(B) 480 mm3
(C) 120 mm3
(D) 840 mm3
702. Identify the triangle:
(A) Equilateral
(B) Scalene
(C) Isosceles
(D) Right
703. The interior angles of a quadrilateral add up to
(A) 180°.
(B) 90°.
(C) 360°.
(D) 270°.
704. Find the volume:
(A) 212 cubic feet
(B) 216 cubic feet
(C) 360 cubic feet
(D) 300 cubic feet
705. Find the volume:
(A) 314 cm3
(B) 7,850 cm3
(C) 785 cm3
(D) 8,850 cm3
706. The formula to find the circumference of a circle is
(A)
(B)
(C)
(D)
707. Find the circumference:
(A) 18.84 meters
(B) 21 meters
(C) 17.75 meters
(D) 18.12 meters
708. Find the volume:
(A) 4,069.44 ft3
(B) 4,960.39 ft3
(C) 1,620 ft3
(D) 4,169.25 ft3
709. Find the volume:
(A) 3,700 cubic inches
(B) 5,000 cubic inches
(C) 250 cubic inches
(D) 3,750 cubic inches
710. Find the diameter:
(A) 12 units
(B) 24 units
(C) 30 units
(D) 25 units
711. Find the area:
(A)
(B)
(C)
(D)
712. Identify the figure:
(A) Pentagon
(B) Quadrilateral
(C) Four-sided triangle
(D) Hexagon
713. Identify the lines that appear to be parallel:
(A) Lines a and c
(B) Lines c and b
(C) Lines a and d
(D) None of the lines are parallel.
714. Find the area of the shaded region:
(A)
(B)
(C) 20 in.2
(D) 16 in.2
715. Find the area:
(A) 100 cm2
(B) 1,000 cm2
(C) 500 cm2
(D) 890 cm2
716. Find the measure of angle d:
(A) 160°
(B) 45°
(C) 35°
(D) 40°
717. Angle b is a(n)
(A) acute angle.
(B) straight angle.
(C) obtuse angle.
(D) reflex angle.
718. Identify the points:
(A) (4, 2), (7, 7)
(B) (2, 4), (7, 7)
(C) (4, 2), (6, 8)
(D) (2, 4), (8, 6)
719. Find the measure of the angle in the shaded portion:
(A) 90°
(B) 270°
(C) 180°
(D) 45°
720. Find the area of the kite:
(A) 45 in.2
(B) 27.5 in.2
(C) 22 in.2
(D) 22.5 in.2
721. Find the measure of the angle:
(A) 43°
(B) 18°
(C) 43.2°
(D) 44°
722. Find the perimeter:
(A) 67 m
(B) 38 m
(C) 68 m
(D) 75 m
723. Find the area:
(A) 81 m2
(B) 47 m2
(C) 75 m2
(D) 78 m2
724. Find the value of a:
(A) 90°
(B) 112°
(C) 45°
(D) Not enough data.
725. Lines x and y are parallel lines. Which angles are congruent angles?
(A)
(B)
(C)
(D) Both A and B
726. Find the area:
(A) 8,199 m2
(B) 819,600 m2
(C) 8,196 m2
(D) 81.96 m2
727. These angles are
(A) congruent.
(B) obtuse.
(C) complementary.
(D) congruent and obtuse.
728. Classify this angle:
(A) Right
(B) Acute
(C) Straight
(D) Reflex
729. Find the surface area:
(A) 2,800 cm2
(B) 2,820 cm2
(C) 2,826 cm2
(D) 2,152 cm2
730. Identify the interior angles:
(A) c, d, e, f
(B) c, d, e, h
(C) f, g, a, b
(D) a, b, f, g
731. Find the measure of angle x:
(A) 112°
(B) 52°
(C) 137°
(D) 189°
732. Find the volume:
(A) 898 in.3
(B) 815 in.3
(C) 964 in.3
(D) 864 in.3
733. Find the measure of angle a:
(A) 118°
(B) 108°
(C) 45°
(D) 120°
734. Find the surface area of the cylinder:
(A) 216 m2
(B) 678.24 m2
(C) 216.85 m2
(D) 678.14 m2
735. The interior angles in a triangle add up to
(A) 90°
(B) 120°
(C) 150°
(D) 180°
736. Find the measure of :
(A) 140°
(B) 120°
(C) 130°
(D) 180°
737. Identify this triangle:
(A) Isosceles
(B) Obtuse
(C) Right
(D) Equilateral
738. Find the measure of angle a:
(A) 15°
(B) 145°
(C) 35°
(D) 25°
739. Find the hypotenuse:
(A) 12 cm
(B) 15 cm
(C) 13 cm
(D) 16.9 cm
740. Find the area of the base:
(A) 290 in.2
(B) 289 in.2
(C) 340 in.2
(D) 329 in.2
741. Find the measure of angle C in the parallelogram:
(A) 60°
(B) 55°
(C) 54°
(D) 50°
742. Find the area if and :
(A) 70 ft2
(B) 24 ft2
(C) 35 ft2
(D) 60 ft2
743. Find the area of the shaded region of the square:
(A) 25 ft2
(B) 90 ft2
(C) 75 ft2
(D) 80 ft2
744. Find the circumference of the circle:
(A) 5 cm
(B) 15.1 cm
(C) 16 cm
(D) 15.7 cm
745. Find the measure of angle A:
(A) 45°
(B) 60°
(C) 75°
(D) 90°
746. Find the measure of angle T:
(A) 84°
(B) 96°
(C) 92°
(D) 87°
747. Find the area:
(A) 9 in.2
(B) 12 in.2
(C) 30 in.2
(D) 11 in.2
748. Find the measure of each arc in the circle, assuming that each sector is equal:
(A) 40°
(B) 36°
(C) 45°
(D) 42.5°
749. Find x:
(A) 41°
(B) 28.5°
(C) 57°
(D) 28°
750. Find the area:
(A) 143.75 in.2
(B) 145.5 in.2
(C) 147.75 in.2
(D) 148 in.2
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