Grade 7 MAP Math Practice — Extreme Challenge (Harder than Typical Grade 8)

Grade 7 MAP Math — Extreme Challenge (Original Items)

Domains: Ratios & Proportional Relationships (RP), The Number System (NS), Expressions & Equations (EE), Geometry (G), Statistics & Probability (SP). Items are original, designed to be tougher than typical Grade 8 MAP problems, and are not actual test questions.

Overview

Challenge tiers: Core (RIT 250–270), Stretch (RIT 270–290), Ultra (RIT 290+).
Skills sampled: multistep percent and proportional reasoning, rational operations with complex fractions and exponents, multi-step equations/inequalities and linear models, circles and composite solids with nets and scale, compound/conditional probability and sampling.

Ratios & Proportional Relationships (RP)

Core (RIT 250–270)

Q1. In a proportional table, x: 3, 7.5, 12 and y: 8.4, 21, 33.6. The constant k = y/x is

RP250–270

Q2. A car goes 156 miles in 2.6 hours. Speed is

58 mph
60 mph
62 mph
65 mph

RP250–270

Q3. 35% of 260 equals

RP250–270

Q4. A scale drawing uses 1 cm : 4 m. A segment of 7.5 cm represents

15 m
20 m
30 m
40 m

RP250–270

Q5. After a 12% discount, a jacket costs $88. Original price was

$98
$100
$102
$110

RP250–270

Q6. A recipe uses sugar:flour = 3:7. If 2.1 kg sugar is used, flour needed is

4.2 kg
4.9 kg
5.6 kg
6.3 kg

RP250–270

Stretch (RIT 270–290)

Q7. If y = 2.4x, then for x = 7.5, y =

16.8
17.5
18.0
18.6

RP270–290

Q8. The bill is $48. Tip is 18%. Total is

$55.44
$56.64
$56.80
$57.24

RP270–290

Q9. From 64 to 80 is a percent increase of

20%
22.5%
25%
30%

RP270–290

Q10. A $100 item is discounted 20%, then increased by 15%. Final price is

RP270–290

Q11. Simple interest on $240 at 6% annual rate for 4 years is

$43.20
$51.20
$57.60
$60.00

RP270–290

Q12. In y = kx, if (x, y) = (12, 30), then k =

RP270–290

Ultra (RIT 290+)

Q13. The unit price is better for which: 18 oz for $5.04 or 24 oz for $6.00?

18 oz for $5.04
24 oz for $6.00
Same
Cannot tell

RP290+

Q14. A measurement is 19 cm; actual is 20 cm. Percent error is

RP290+

Q15. 5 notebooks cost $11.75. Cost of 17 notebooks is

$38.95
$39.95
$40.00
$41.65

RP290+

Q16. A mixture is 30% juice. How much pure juice to add to 800 mL to make it 40%?

80 mL
120 mL
133 mL
200 mL

RP290+

Q17. A store marks up $32 by 35% then applies a 10% coupon to the marked price. Final price is

$38.88
$39.50
$40.32
$41.04

RP290+

Q18. If y varies inversely with x and y = 6 when x = 4, then when x = 12, y =

RP290+

Q19. Red:blue = 4:11. If there are 300 in total, blue =

RP290+

Q20. Successive changes: +25% then −20%. Net percent change is

RP290+

The Number System (NS)

Core (RIT 250–270)

Q21. 0.36 ÷ 0.09 =

NS250–270

Q22. 7/8 − 5/12 =

1/6
5/24
11/24
13/24

NS250–270

Q23. (−2)^3 + 5(−1) =

−13
−7
−3
3

NS250–270

Q24. |−8| − |−3| =

−11
−5
5
11

NS250–270

Q25. 2/3 ÷ 5/6 =

NS250–270

Q26. 0.27 as a fraction in simplest form is

27/100
3/10
27/90
9/40

NS250–270

Stretch (RIT 270–290)

Q27. (−3)^4 × (−3) =

−81
−27
27
81

NS270–290

Q28. 5/12 + 7/18 =

2/3
29/36
31/36
5/6

NS270–290

Q29. √65 is between

7 and 8
8 and 9
9 and 10
10 and 11

NS270–290

Q30. (1.2 × 10^3) × (3 × 10^−2) =

3.6 × 10^1
3.6 × 10^2
3.6 × 10^3
3.6 × 10^4

NS270–290

Q31. 0.4 repeating (0.444…) equals

NS270–290

Q32. |−5 + 2| + |−3| =

NS270–290

Ultra (RIT 290+)

Q33. (−1.5)^2 − (−2)^3 =

−4.25
3.75
6.25
8.25

NS290+

Q34. 3/5 ÷ 7/10 =

3/7
6/7
7/6
10/21

NS290+

Q35. Evaluate: 2(−3)^2 − 4(−3) + 1

NS290+

Q36. Which is greater: −0.7 or −3/5?

−0.7
−3/5
Equal
Cannot tell

NS290+

Q37. 1 3/4 × 2 2/5 =

3 1/2
4 1/5
4 1/5
4 3/20

NS290+

Q38. (−2)^0 + 5^0 equals

0
1
2
Undefined

NS290+

Q39. 1.2 × (−0.5) − 0.8 × (−0.5) =

−1.0
−0.2
0
0.2

NS290+

Q40. 3^(−2) equals

−9
−1/9
1/9
9

NS290+

Expressions & Equations (EE)

Core (RIT 250–270)

Q41. Solve: 4x − 7 = 21

EE250–270

Q42. Evaluate: 3(2 + 5) − 4

EE250–270

Q43. If x = 2 and y = 3, 2x^2 + y equals

EE250–270

Q44. Solve: x/6 = 8/3

EE250–270

Q45. Which value satisfies x/3 > 4?

EE250–270

Q46. 18 − 2(5 + 1) =

EE250–270

Stretch (RIT 270–290)

Q47. Solve: 4x − 3(x − 2) = 19

EE270–290

Q48. Solve: 7 − (2x − 3) = 12

−2
−1
1
2

EE270–290

Q49. If y = 2x + 1, then for x = −3, y =

−7
−5
−3
5

EE270–290

Q50. Solve: x/3 + x/2 = 10

EE270–290

Q51. Slope between (−1, 2) and (5, 14) is

EE270–290

Q52. Evaluate 2(3x − 4) − (x + 5) when x = 3

−2
0
2
4

EE270–290

Ultra (RIT 290+)

Q53. Solve: 5 − 2(3x − 4) = 19

−2
−1
1
2

EE290+

Q54. If f(x) = 2x^2 − x, then f(−3) =

EE290+

Q55. Solve the inequality: 3(x − 2) ≤ 2x + 7

x ≤ 11
x ≥ 11
x ≤ 13
x ≥ 13

EE290+

Q56. Solve: (x − 1)/5 = (2x + 3)/10

x = −5
x = 5
Infinitely many solutions
No solution

EE290+

Q57. Simplify: (3^2)(3^4) ÷ 3^3

EE290+

Q58. Solve: (2/3)x − 4 = 5

9
12
13.5
27

EE290+

Q59. The y-intercept of y = −3x + 7 is

−7
−3
0
7

EE290+

Q60. If 2x − y = 7 and x + y = 5, then x =

EE290+

Geometry (G)

Core (RIT 250–270)

Q61. Circumference of a circle with radius 7 (π ≈ 3.14) is

21.98
43.96
153.86
49.00

G250–270

Q62. Area of a circle with diameter 10 (π ≈ 3.14) is

31.4
62.8
78.5
157.0

G250–270

Q63. The complement of 62° is

18°
28°
118°
128°

G250–270

Q64. With parallel lines, angle x is alternate interior to 115°. Then x =

65°
70°
90°
115°

G250–270

Q65. Scale 1 in : 6 ft. A drawing length of 3.5 in represents

18 ft
20 ft
21 ft
24 ft

G250–270

Q66. A right triangle has legs 6 and 8. Its perimeter (with hypotenuse) is

G250–270

Stretch (RIT 270–290)

Q67. Surface area of a cube with side 3 is

G270–290

Q68. Area of a 12 × 5 rectangle with a semicircle of radius 5 attached on one side (π ≈ 3.14) is about

85.0
94.2
99.3
110.0

G270–290

Q69. Similar triangles have corresponding sides 6→8 and 9→x. Then x =

G270–290

Q70. Distance between (−2, 5) and (3, −1) is approximately

G270–290

Q71. Area of a ring (annulus) with outer radius 6 and inner radius 4 (π ≈ 3.14) is about

31.4
50.3
62.8
78.5

G270–290

Q72. Surface area of a 2 × 3 × 4 rectangular prism is

G270–290

Ultra (RIT 290+)

Q73. Arc length of a 60° sector in a circle of radius 12 (π ≈ 3.14) is about

6.28
12.57
18.85
25.13

G290+

Q74. Two complementary angles measure (x + 20)° and (2x + 10)°. The larger angle is

40°
45°
50°
60°

G290+

Q75. A dilation centered at the origin with scale factor 1.5 sends (−4, 2) to

(−6, 3)
(−5, 2.5)
(−3, 1)
(6, −3)

G290+

Q76. If a circle has circumference 31.4, then its radius (π ≈ 3.14) is

G290+

Q77. A triangle’s side lengths are scaled by a factor of 3. Its area is multiplied by

G290+

Q78. A right triangle has a leg of 9 and hypotenuse of 15. The other leg is

G290+

Q79. Volume of a cylinder radius 3, height 8 (π ≈ 3.14) is about

75.4
113.0
226.1
452.2

G290+

Q80. Surface area of a cylinder radius 4, height 10 (π ≈ 3.14) is about

175.8
201.1
351.7
402.1

G290+

Statistics & Probability (SP)

Core (RIT 250–270)

Q81. A bag has 4 red and 6 blue marbles. P(red) =

SP250–270

Q82. How many outcomes are in the sample space for flipping 3 coins?

SP250–270

Q83. P(roll > 4) on a fair die equals

SP250–270

Q84. Mean of 5, 7, 9 is

SP250–270

Q85. Relative frequency of success is 18 out of 60. As a percent it is

SP250–270

Q86. Median of 2, 3, 5, 8, 11, 12 is

SP250–270

Stretch (RIT 270–290)

Q87. In 100 spins, red appears 28 times. An estimate of P(red) is

0.18
0.25
0.28
0.38

SP270–290

Q88. If P(A) = 0.37, then P(not A) =

0.37
0.47
0.57
0.63

SP270–290

Q89. For independent events with P(A) = 0.4 and P(B) = 0.5, P(A and B) =

0.10
0.20
0.40
0.90

SP270–290

Q90. Which is a simple random sample?

Survey the math club
Ask every 10th student entering school
Ask only your friends
Ask morning students only

SP270–290

Q91. P(sum is even) when rolling two dice is

1/3
5/12
1/2
2/3

SP270–290

Q92. Toss two fair coins. P(at least one head) is

SP270–290

Ultra (RIT 290+)

Q93. Without replacement from 5 red and 3 blue, P(two red in a row) =

5/28
5/21
5/14
3/7

SP290+

Q94. Number of outcomes choosing an ordered pair from {A, B, C} × {1, 2, 3, 4} is

SP290+

Q95. The mean of 5 numbers is 10. If one value increases by 3, the new mean is

10.3
10.6
11
13

SP290+

Q96. For data 4, 8, 8, 10, 12, the IQR is

SP290+

Q97. From a bag with 4 red and 6 blue, P(second red | first blue) =

SP290+

Q98. A class has 12 girls and 18 boys. Two students are chosen without replacement. P(both girls) =

2/15
22/145
11/145
66/145

SP290+

Q99. The probability of a complement is 0.18. The event’s probability is

0.18
0.32
0.72
0.82

SP290+

Q100. Drawing a number 1–20, the probability it is prime is

1/5
2/5
3/10
1/2

SP290+

Answer Key

1:B, 2:C, 3:C, 4:C, 5:D, 6:C, 7:D, 8:B, 9:C, 10:B, 11:C, 12:C, 13:A, 14:B, 15:D, 16:D, 17:A, 18:B, 19:D, 20:B, 21:D, 22:D, 23:B, 24:C, 25:B, 26:A, 27:A, 28:C, 29:B, 30:A, 31:B, 32:D, 33:D, 34:B, 35:C, 36:B, 37:D, 38:C, 39:D, 40:C, 41:C, 42:B, 43:C, 44:D, 45:C, 46:A, 47:C, 48:D, 49:B, 50:C, 51:A, 52:A, 53:D, 54:C, 55:A, 56:B, 57:B, 58:C, 59:D, 60:C, 61:B, 62:C, 63:B, 64:D, 65:C, 66:D, 67:B, 68:C, 69:B, 70:C, 71:B, 72:C, 73:C, 74:C, 75:A, 76:B, 77:D, 78:C, 79:C, 80:D, 81:B, 82:B, 83:C, 84:C, 85:B, 86:C, 87:C, 88:D, 89:B, 90:B, 91:C, 92:B, 93:B, 94:C, 95:A, 96:B, 97:B, 98:B, 99:D, 100:B

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Map Grade 7 Practice Test

Grade 7 MAP Math — Extreme Challenge (Original Items)

Overview

Ratios & Proportional Relationships (RP)

Core (RIT 250–270)

Stretch (RIT 270–290)

Ultra (RIT 290+)

The Number System (NS)

Core (RIT 250–270)

Stretch (RIT 270–290)

Ultra (RIT 290+)

Expressions & Equations (EE)

Core (RIT 250–270)

Stretch (RIT 270–290)

Ultra (RIT 290+)

Geometry (G)

Core (RIT 250–270)

Stretch (RIT 270–290)

Ultra (RIT 290+)

Statistics & Probability (SP)

Core (RIT 250–270)

Stretch (RIT 270–290)

Ultra (RIT 290+)

Answer Key