Mathematics Diagnostic Exam for Incoming Grade 11 Learners
Answer the following questions. Choose the letter of the correct answer.
1. What is the sum of the integers 4, -8, 13 and -15?
A. -5
B. -6
C. -7
D. -8
C. 640
D. 620
C. 8
D. -9
2. Solve for the product of 4, -10 and -16.
A. -640
B. -620
3. Find the quotient of 81 divided by -9.
A. 6
B. -7
4. Determine the difference of the integers 5, -2, 8 and -1.
A. -2
B. -1
C. 0
D. 1
5. What happens to the quotient when you divide integers with like signs?
A. in becomes positive
C. It assumes the sign of the denominator
B. it becomes negative
D. it assumes the sign of the numerator
3
4
1
4
6. What is the sum of 𝑎𝑛𝑑 ?
A. 1
7. Find the difference of
A.
5
12
B.
4
8
B.
2
12
D.
1
2
1
6
D.
2
3
11
5
D.
13
5
C. 2
1
− .
4
8
48
C.
2
5
8. What do you need to add to to make it equal to 3?
A.
8
5
9. What is half of
A.
B.
38
5
C.
?
76
5
10. Evaluate the product of
A.
15
5
42
88
B.
25
10
C.
18
10
D.
27
5
21
44
C.
19
66
D.
32
77
6 7
∙ .
11 8
B.
11. What is the simplified form of the expression 9𝑥 − (3𝑦 − 8𝑥) + 2𝑦?
A. 5𝑥 − 2𝑦
12. Simplify the expression
A. 𝑥 − 2
B. 15𝑥 + 6𝑦
C. 17𝑥 − 2𝑦
D. 17𝑥 − 𝑦
C. 𝑥 + 4
D. 𝑥 + 5
𝑥 2 +2𝑥−15
.
𝑥−3
B. 𝑥 + 6
13. Give the factors of (36 − 𝑥 2 ).
A. (𝑥 + 3)(𝑥 − 3)
B. (6 + 𝑥)(6 − 𝑥)
C. (𝑥 + 12)(𝑥 − 3)
D. (𝑥 + 6)(𝑥 − 6)
14. Solve the polynomial 6𝑥 3 + 3𝑥 2 − 27𝑥 in factored form.
A. 3𝑥(2𝑥 2 + 𝑥 − 9)
B. 3(2𝑥 3 + 𝑥 − 9)
C. 3𝑥 2 (2𝑥 + 𝑥 − 9)
D. 3𝑥(2𝑥 2 + 3𝑥 − 9)
15. Determine the factors of 6𝑥 2 + 𝑥 − 2.
A. (𝑥 + 2)(𝑥 − 1)
B. (2 + 6𝑥)(1 − 𝑥)
C. (2𝑥 − 1)(3𝑥 + 2)
D. (3𝑥 + 1)(2𝑥 − 2)
C. 𝑥 = 6 ± √42
D. 𝑥 = 4 ± √42
16. Solve the quadratic equation 𝑥 2 − 10𝑥 − 18 = 0.
A. 𝑥 = 7 ± √43
B. 𝑥 = 5 ± √43
17. Find the solution for the quadratic equation 𝑥 2 − 2𝑥 − 7 = 0.
A. 𝑥 = 2 ± √4
B. 𝑥 = 1 ± √3
C. 𝑥 = 2 ± √2
D. 𝑥 = 1 ± 2√2
18. What is the quadratic equation solution for 𝑥 2 + 6𝑥 + 1 = 0?
A. 𝑥 = −3 ± 2√2
B. 𝑥 = 3 ± √2
C. 𝑥 = −3 ± 3√2
D. 𝑥 = 3 ± 2√3
19. Determine the solution for the quadratic equation 𝑥 2 + 10𝑥 − 7 = 0.
A. 𝑥 = −5 ± 2√2
B. 𝑥 = 5 ± 2√4
C. 𝑥 = −5 ± 4√2
D. 𝑥 = 5 ± √42
20. Evaluate the solution of the quadratic equation 𝑥 2 + 8𝑥 + 2 = 0.
A. 𝑥 = −4 ± √4
B. 𝑥 = 4 ± √14
C. 𝑥 = −4 ± √14
D. 𝑥 = 4 ± 2√2
C. 𝑥 = 25
D. 𝑥 = 30
C. 𝑥 = 10
D. 𝑥 = −8
21. Given 𝑥 + 5 = 25, solve for the value of 𝑥.
A. 𝑥 = 20
B. 𝑥 = 15
22. Given 2𝑥 = 16, solve for the value of 𝑥.
A. 𝑥 = 4
B. 𝑥 = 8
4
𝑥
23. Given 20 = , solve for the value of 𝑥.
A. 𝑥 = 10
B. 𝑥 =
1
8
C. 𝑥 =
1
6
D. 𝑥 =
1
5
𝑥
3
24. Given = 15, solve for the value of 𝑥.
A. 𝑥 = 10
B. 𝑥 = 15
C. 𝑥 = 45
D. 𝑥 = 35
C. 𝑥 = 16
D. 𝑥 = 20
1
4
25. Given 𝑥 = 8, solve for the value of 𝑥.
A. 𝑥 = 32
B. 𝑥 = 12
26. The bottom of a ladder must be placed 3 feet from a wall. The ladder is 12 feet long. How far above the ground
does the ladder touch the wall?
A. 3√15𝑓𝑡.
B. 3√5𝑓𝑡.
C. 3√25𝑓𝑡.
D. 2√15𝑓𝑡.
27. A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner
to the corner diagonally across the field. How far do the players run?
A. 90𝑚.
B. 100𝑚.
C. 150𝑚.
D. 200𝑚.
28. How far from the base of the house do you need to place a 15ft. ladder so that it exactly reaches the top of a
12ft. wall?
A. 9𝑓𝑡.
B. 10𝑓𝑡.
C. 15𝑓𝑡.
D. 12𝑓𝑡.
29. What is the length of the diagonal of a 10 cm by 15 cm rectangle?
A. 3√15𝑐𝑚.
B. 5√13𝑐𝑚.
C. 3√25𝑐𝑚.
D. 5√3𝑐𝑚.
30. The diagonal of a rectangle is 25 in. The width is 15 in. What is the area of the rectangle?
A. 400𝑖𝑛2 .
B. 150𝑖𝑛2 .
C. 200𝑖𝑛2 .
D. 300𝑖𝑛2 .
31. Simplify the given expression 4𝑟 −3 ∙ 2𝑟 2
A.
𝑟
8
B.
4
𝑟
C.
8
𝑟
D. 8𝑟
32. Apply the law of exponents to the given expression (4𝑟 0 )4
A. 256𝑟
B.
16
𝑟
33. Simplify the given expression
A.
𝑛
3
C. 256
D. 64
C. 𝑛2
D. 3𝑛
3𝑛4
3𝑛3
B. 𝑛
2𝑥 3
𝑦
34. Apply the law of exponents to the given expression ( )
A.
8𝑥 3
𝑦
B.
4𝑥 3
C.
𝑦2
8𝑥 3
𝑦3
D.
6𝑥 3
𝑦2
2
35. Simplify the given expression
A.
1
𝑎2
B.
(𝑎2 )
𝑎6
1
𝑎
C.
2
𝑎2
D. 𝑎2
C.
21
25
D.
3
4
C.
16
30
D.
3
4
36. Determine the value of Tan (Z) on the figure:
A.
28
35
B.
21
28
37. Solve for the value of Cos (C) on the figure:
A.
8
17
B.
30
34
38. Evaluate the value of Sin (C) on the figure:
A.
8
7
B.
35
21
C.
4
5
D.
21
28
39. Find the value of Tan (X) on the figure:
A.
32
40
B.
32
24
C.
4
3
C.
34
16
D.
3
4
40. Determine the value of Cos (A) on the figure:
A.
15
17
B.
30
34
For questions 41 to 45, base your answers on the given Cartesian plane below.
D.
16
30
41. Give the coordinates of point A.
A. (-7, -5)
B. (2, 5)
C. (-10, 2)
D. (1, -5)
C. (-10, 2)
D. (1, -5)
C. (-10, 2)
D. (1, -5)
C. (-10, 2)
D. (1, -5)
C. (2, -4)
D. (2, -5)
C. −√6
D. 2√3
C. −√3
D. 2√7
C. 5√10
D. 2√3
42. Give the coordinates of point J.
A. (-7, -5)
B. (2, 5)
43. Give the coordinates of point H.
A. (-7, -5)
B. (2, 5)
44. Give the coordinates of point E.
A. (-7, -5)
B. (2, 5)
45. Give the coordinates of point C.
A. (-8, -3)
B. (-8, -8)
46. Evaluate the given expression 3√6 − 4√6.
A. √6
B. 2√6
47. Solve the given expression −2√3 + 3√27.
A. 7√3
B. −3√7
48. Simplify the given expression √5 ∙ 2√2.
A. 3√12
B. 2√10
49. Calculate the given expression
A.
√5
√3
50. Solve the given expression
A.
1
6
√25
.
√15
B. 3√5
C.
√15
√3
D.
√15
3
√3
3
D.
√3
9
2√3
.
4√27
B. 2√3
C.
ANSWER KEY:
1.B
34.C
2.C
35.A
3.D
36.D
4.C
37.A
5.A
38.C
6.A
39.C
7.C
40.A
8.D
41.C
9.A
42.A
10.B
43.B
11.D
44.D
12.D
45.A
13.B
46.C
14.A
47.A
15.C
48.B
16.B
49.D
17.D
50.A
18.A
19.C
20.C
21.A
22.B
23.D
24.C
25.A
26.A
27.C
28.A
29.B
30.D
31.C
32.C
33.B