25 EQAO Ontario Grade 9 Math Questions – Diagnostic & Practice Set by Tutorone

If the tank is ¼ empty, it must be ¾ full: 3/4 the total capacity of 20 gallons is 15

The value of choice (A) is \( frac{11}{12} \), the value of choice (B) is \( frac{5}{12} \), the value of choice (C) is \( frac{1}{3} \) or \( frac{4}{12} \), the value of choice (D) is \( frac{1}{4} \) or \( frac{3}{12} \), and the value of choice (E) is \( frac{1}{3} \) or \( frac{4}{12} \). Therefore, choice (D) has the least value.

If \( x + (x + 3) > 35 \), then \( 2x > 32 \). So \( x > 16 \). The only answer that is appropriate is

The perimeter of a square is found by summing the lengths of each side. Because the lengths are equal on a square, you can multiply one side by 4 to get the perimeter. Therefore, \( 4s = 100 \), so \( s = 25 \).

To find the greatest value of the four, assume the remaining three values are the least possible positive integers, 1. The average then is \( frac{1 + 1 + 1 + x}{4} = 7 \). Solve for \( x \). \( 3 + x = 28 \), so \( x = 25 \).

Round $9.95 to $10.00 and find 40% of 10. \( 40% = frac{40}{100} = 0.40 \). \( 0.40 times 10 = 4 \).

Four students make up one fifth of a class. Translating this into a mathematical equation, you get \( frac{1}{5} times c = 4 \). Solving for \( c \), \( c = 4 times 5 = 20 \).

Let \( d \) represent Don's age now and \( d + 7 \) represent Don's age in 7 years. Let \( p \) represent Peter's age now. Set up mathematical equations for the problem. \( d = p + 8 \), and \( d + 7 = 2p \). Substituting \( d = p + 8 \) into the second equation: \( (p + 8) + 7 = 2p \), solving gives \( p + 15 = 2p \), so \( p = 15 \).

Set up a ratio for this problem and solve: \( p \) represents the number of pieces of candy purchased for \( c \) cents (\( frac{p}{c} \)). 20 pieces of candy can be purchased for \( x \) cents (\( frac{20}{x} \)). Using cross-multiplication, \( px = 20c \), so \( x = frac{20c}{p} \).

$4,500,000 is \( t \) times greater than $75,000. \( 4,500,000 = 75,000t \), so \( t = frac{4,500,000}{75,000} = 60 \).

This is a 45-45-90 triangle. Since this is true, the base is also 5 units long. By the Pythagorean Theorem, \( v^2 = 5^2 + 5^2 = 25 + 25 = 50 \).

Let \( o \) represent the amount of oats eaten and \( g \) the amount of grass eaten. Since 1.5 times as many pounds of oats are eaten as grass, we have \( o = frac{3}{2} g \). The total amount eaten is \( o + g = 30 \). Substituting the value of \( o \) into the equation gives \( frac{3}{2} g + g = 30 \), so \( frac{5}{2} g = 30 \), and \( g = 12 \).

First, solve for \( x \): \( 2x - 4 = 50 \), so \( 2x = 54 \), and \( x = 27 \). Now, \( frac{x}{9} = frac{27}{9} = 3 \).

There are 180° in a triangle and 360° in a rectangle (made up of four 90° angles). The difference is \( 360^{circ} - 180^{circ} = 180^{circ} \). One half of \( 180^{circ} \) is \( 90^{circ} \).

Let \( g \) represent the number of gorillas, and let \( t \) represent the number of tigers. Since there are 3 times as many gorillas as tigers, \( g = 3t \). There are 3 more tigers than zebras, so \( t = z + 3 \). Substituting this into the equation for \( g \), we get \( g = 3(z + 3) = 3z + 9 \).

Doubling the denominator of a fraction divides the value by 2. Halving one of the factors in the numerator also halves the value of the fraction. Doing both divides the original value by 4.

Since 10% is \( frac{1}{10} \), multiply 40 by 10 to find the full amount: \( 40 times 10 = 400 \).

100 is 20 larger than 80. 20 is one fourth, or 25%, of 80. Therefore, 125% of 80 is equivalent to 100.

40 inches equals \( 3frac{1}{3} \) feet. Since \( frac{1}{8} \) inch represents 1 foot, multiply \( frac{1}{8} \) by 3.33 to get approximately \( 1frac{1}{4} \) inches.

Bracket the multiplication and division first, and solve the problem: \( (6 times 2) / 3 + (1/3 times 9) = 12 / 3 + 3 = 4 + 3 = 7 \).

Since \( x + 3 < 12 \), we can subtract 3 from both sides, giving us \( x < 9 \). Thus, \( x \) can be any number less than 9.

Substituting the values into the expression: \( sqrt{16 + 36 + 3} = sqrt{55} \), which is approximately \( 7.42 \).

To find the average, sum the numbers and divide by the number of addends: \( frac{-3 + 17 + 0 - 1 + 12}{5} = frac{25}{5} = 5 \).

If we substitute \( A = -3 \), the denominator of the fraction becomes zero. A denominator of zero is undefined in mathematics.

Simply move the decimal point one place to the left: \( 1011 div 10 = 101.1 \).