GRADE 9 MATH QUESTIONS

Problem 1 :

Find the value of k, if x – 1 is a factor of

4x³ + 3x² – 4x + k

(A) -3      (B) -5     (C) 0

Solution

Problem 2 :

What is the value of the expression given below?

³√4  x  ³√16

(A) 3      (B) 4     (C) 2

Solution

Problem 3 :

Find the area of the quadrilateral whose diagonal measures the length of 50 m and the perpendicular distance measures 10 m and 20 m respectively.

(A) 7.50 sq.m      (B) 75 sq.m      (C) 750 sq.m

Solution

Problem 4 :

Cost of leveling a land is $12 per square meter. A land is in the form of a trapezium whose parallel sides are of lengths 18m and 12 m. If its other two sides are each of length 5m, find the total cost incurred in leveling the land

(A) 230     (B) 540       (C) 720

Solution

Problem 5 :

The perimeter of a rhombus is 20 cm. One of the diagonals is of length 8 cm. Find the length of the other diagonal and the area of the rhombus.

(A) 50 sq.cm     (B) 32 sq.cm      (C) 24 sq.cm

Solution

Problem 6 :

Evaluate the following log ₂ 64 + log ₂ 4

(A) 4        (B) 8      (C) 6

Solution

Problem 7 :

Two sets are called ____________ if they have same elements.

(A) Equivalent sets     (B) Null set     (C) Equal sets

Solution

Problem 8 :

Find the perimeter of the sector whose area is 924 sq.cm and the central angle is 240.

(A) 100 cm     (B) 115 cm     (C) 130 cm

Solution

Problem 9 :

Factorize 3x²   - 18xy

(A) 3x (x-6y)     (B) 3 x (x-18y)    (C) 3 (x²-18y)

Solution

Problem 10 :

Solve

3(x + 4) + 2 (y - 3) = 17

and

7(x - 3) - 3 (y + 4)  =  8

(A) (8,1)      (B) (5,-2)    (C) (0,6)

Solution

Problem 1 :

Which of the following is an equivalent form of the expression

15 x + 24 ax ?

A) 39ax²  B) 39 (a + 2x)   C) (5 + 8a)x   D) (15 + 24 a) x

Solution

Problem 2 :

The formula d = rt is used to calculate the distance an object travels over a period of time, at a constant rate, r. Based on this formula, what is the rate, r, in terms of d and t ?

A) r = d/t   B) r = dt     C) r = t/d    D) r = d - t

Solution

Problem 3 :

Which of the following ordered pairs (x , y) satisfies both equations y = x² + 3 x − 4 and x = y − 4 ?

A) (0, −4)     B) (2, 6)     C) (3, 14)    D) (5, 9)

Solution

Problem 4 :

Which of the following is a solution to the equation

2x² + 4x = 3 + 3x² ?

A) −1    B) 0     C) 3     D) 6

Solution

Problem 5 :

−3x − 4 y = 20

x − 10 y = 16

If (x, y) is the solution to the system of equations above, what is the value of x ?

A) −14     B) −12    C) −4     D) 16

Solution

Problem 6 :

The equation y = 36 + 18x models the relationship between the height y, in inches, of a typical golden delicious apple tree and the number of years, x, after it was planted. If the equation is graphed in the xy-plane, what is indicated by the y-intercept of the graph?

A) The age, in years, of a typical apple tree when it is planted

B) The height, in inches, of a typical apple tree when it is planted

C) The number of years it takes a typical apple tree to grow

D) The number of inches a typical apple tree grows each year

Solution

Problem 7 :

Giovanni wants to buy shirts that cost $19.40 each and sweaters that cost $24.80 each. An 8% sales tax will be applied to the entire purchase. If Giovanni buys 2 shirts, which equation relates the number of sweaters purchased, p, and the total cost in dollars, y ?

(A) 1.08 (38.80 + 24.80 p) = y

(B) 38.80 + 24.80 p = 0.92 y

(C) 38.80 + 24.80 p = 1.08 y

(D) 8 (0.92 38.80 + 24.80 p) = y

Solution

Problem 8 :

A line is graphed in the xy-plane. If the line has a positive slope and a negative y-intercept, which of the following points cannot lie on the line?

A) (−3, −3)    B) (−3, 3)     C) (3, −3)    D) (3, 3)

Solution

Problem 9 :

A parachute design uses 18 separate pieces of rope. Each piece of rope must be at least 270 centimeters and no more than 280 centimeters long. What inequality represents all possible values of the total length of rope x, in centimeters, needed for the parachute?

A) 270 ≤ x ≤ 280      B) 4,860 ≤ x ≤ 4,870

C) 4,860 ≤ x ≤ 5,040      D) 5,030 ≤ x ≤ 5,040

Solution

Problem 10 :

A carpenter has $60 with which to buy supplies. The carpenter needs to buy both nails and screws. Nails cost $12.99 per box, and screws cost $14.99 per box. If n represents the number of boxes of nails and s represents the number of boxes of screws, which of the following systems of inequalities models this situation?

A) 1 2.99 n + 14.99 s ≥ 60, n +s ≤1

B) 1 2.99 n + 14.99 s ≤ 60, n +s ≤1

C) 12.99 n + 14.99 s ≥ 60, n ≥1 and s ≥1

D) 12.99 n + 14.99 s ≤ 60, n ≥1 and s ≥1

Solution

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