SHSAT MATH PRACTICE ONLINE WORKSHEET

(1)  In the sequence of numbers 1, 2, 2, 3, 3, 3,. . . [assume the pattern of one 1, two 2s, three 3s, four 4s, and so on continues], the number in the 40^th position will be

(A)  8  (B)  9  (C)  10  (D)  11  (E)  40

Solution

(2)  Each side of a square is an integral number of inches, and its area is 576 square inches.  If each side of the square is increased by 1 foot, forming a new square, the area of the new square, in square inches, is

(A)  577  (B)  588  (C)  720  (D)  1,296 

(E)  not determined

Solution

(3)  Let P = 18/25, Q = 5/7, and R = 3/4.  Then

(A)  P < Q < R  (B)  P < R < Q  (C)  Q < P < R

(D)  Q < R < P  (E)  R < P < Q

Solution

(4)  A water container is 3/4 full.  After 20 ounces of water is removed, the container is 1/4 full.  How many ounces of water does a full container hold?

(A)  20  (B)  40  (C)  60  (D)  80  (E)  100

Solution

(5) For how many integer values of n will the expression (n-10) / (14-n) have a positive value?

(A)  0  (B)  1  (C)  3  (D)  4  (E)  5

Solution

(6) The function f is defined by f(x) = 3x - 40. If f(a) = 8, what is the value of a ?

(A)  -96  (B)  -16  (C)  16  (D)  -32/3  (E)  32/3

Solution

(7) If triangle ABC, if AB = 1 and BC = 100, which of the following must be true about the angles ?

A) The measure of ∠A is greatest.

B) The measure of ∠B is greatest

C) The measure of ∠A and ∠B are equal

D) The measure of ∠C is greatest

E) The measure of ∠C is least.

Solution

(8) Each time Sue rents a bicycle, she pays a fixed base cost plus an hourly rate for the time the bicycle is rented. Last Saturday she paid $12 to rent a bicycle for 6 hours and yesterday she paid $9.50 to rent a bicycle for 4 hours. Which of the following equations shows the total cost C in dollars for Sue to rent a bicycle for n hours ?

A) C = 1.25n     B) C = 1.25n + 4.50

C) C = 2n + 2.50    D)  C = 2.5n + 2    E) C = 4.5n + 1.25

Solution

(1)

A square of side 4 is topped by a semicircle, as shown.  Point P is the center of the arc at the top.  Then the shaded area is equal to

(A)  π + 2  (B)  (π/2) + 2  (C)  2π + 2

(D)  2π – 4  (E)  2π + 4

Solution

(2)  (4⁶ x 3⁴ x 2²) / (4² x 3⁴ x 2⁶) =

 (A)  1  (B)  2  (C)  8  (D)  16  (E)  24

Solution

(3) Which one of the following numbers is less than 1/3?

(A)  1111/3333  (B)  299/895  (C)  .1 x 4 

(D)  .4 x 1  (E)  5! / 6!

Solution

(4)  The ratio of a to b is 3 to 4.  The ratio of b to c is 5 to 6.  The ratio of a to c is

(A)  9:10  (B)  5:8  (C)  1:2  (D)  2:5  (E)  none of these

Solution

(5)

(All lines shown are either vertical or horizontal)  If x and y are integers, and the shaded area is 52, then the perimeter of the figure is

         (A)  20  (B)  24  (C)  52  (D)  56  (E)  196

Solution

(6) In 1954 the record time for running a mile was 4 minutes and by 1975 the record had fallen to 3 minutes and 50 seconds. If the record had fallen at a constant rate during that time and continued to do so, in what year can it be expected that the record time for running a mile will be 3  1/2 minutes ?

Solution

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

a) (0, -4)   b) (2, 6)     c) (3, 14)     d)  (5, 9)

Solution

(8) The formula d = tr is used to calculate the distance an object travels over a period of time, t, 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

(9) 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 + 24.80p) = y

b) 38.80 + 24.80 p = 0.92y

c) 38.80 + 24.80 p = 1.08y

d) 0.92 (38.80 + 24.80p) = y

Solution

(1)  One-half of one-sixth is equal to

(A)  one-third of one-fourth  (B)  one-third 

(C)  one  (D)  two  (E)  three

Solution

(2)  The areas of triangles ABC and XYZ are each 10.  The area of the shaded region is 14.  Then the area of triangle XWC is

(A)  12  (B)  8  (C)  6  (D)  3  (E)  2

Solution

(3) 1  1/10  + 2  11/100 + 3  111/1000 (mixed fractions)  =

(A)  6.111  (B)  6.123  (C)  6.111111  (D)  6.321  (E)  6.6

Solution

(4)  If x is positive and x² + x = 50, then x is a number between

(A)  6 and 7  (B)  7 and 8  (C)  8 and 9 

(D)  9 and 10  (E)  10 and 11

Solution

(5)  In the figure, C is a point on line segment AE.  If AB = BC, what is the measure of angle DCE?

(A)  80°  (B)  75°  (C)  60°  (D)  25°  (E)  20°

Solution

(6) Which of the following is a solution to the equation 

2x² + 4x = 3 + 3x²

a) -1    b) 0     c) 3     d) 6

Solution

(7) 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

(8) A line is graphed in the -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

(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

(10) 

In the figure, which of the following ratios has the same value as AB/BC ?

A)  BD/DC    B) BC/AC     C) AD/BD     D) DC/BC

Solution

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