Grade 11 Math Practice Test Questions
Grade 11 math practice test questions are presented along with their solutions on videos.
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Simplify the following expressions
Solution on video at Simplify Square Root Expressions question 1
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Simplify the following expression
Solution on video at Simplify Square Root Expressions Using the Conjugate question 2
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Expand and simplify the following expression
Solution on video at Expand and Simplify Polynomials , question 3
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b and x are positive real numbers such that
Find x .
Solution on video at Solve Equations with Square Roots , question 4
\( \)\( \)\( \)\( \)
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Simplify and express as a single rational expression (2 parts a and b)
a) \( \quad \displaystyle \frac{2x}{x-1}\:-\:\frac{1}{x+2}-\frac{6}{2x^2+2x-4} \).
Solution on video at Add Rational Expressions and Simplify, question 5 a
b) \( \quad \displaystyle \frac{2x^2+2x-4}{x^2+8x+15} \div \frac{2x^2+6x+4}{x^2+10x+21} \).
Solution on video at Divide Rational Expressions and Simplify , question 5 b
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Simplify the expression and write the result with positive exponents only.
\( \quad \displaystyle \frac{(3 \: x^2 y^2)^2}{(- 2 \: x y^2)^4} \:\div \:\frac{(3 \: x y)^3}{(6 \: x^{-1} y^2)^2} \).
Solution on video at Simplify Rational Expression with Expoenents, question 6
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Solve the quadratic inequality \( -x^2-2x \gt - 2 \)
Solution on video at solve quadratic inequalities, question 7
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Let \( f(x) = - x^2 + 2 x + 2 \).
a) Find the vertex of the graph of \( f \)
b) Find the x and y intercepts of the graph of \( f \)
c) Find the equation of the axis of symmetery of the graph of \( f \)
d) What are the domain and range of \( f \) ?
d) Graph \( f \).
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a) Find the equation of the quadratic function \( f \) whose graph is shown below and write it in the form \( f(x) = a x^2 + b x + c \).
b) Find the exact values of the x intercept of the graph of \( f \).
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Find the equation of the exponential function of the form \( g(x) = a^{x-b} \), where \( a \) and \( b \) are constants to be found, and whose graph is shown below.
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Solve the equation
\( \displaystyle \frac{2x+1}{x-2}\:=-1\:-\:\frac{1}{x+1} \).
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Use special angles and trigonometric formulas to find the exact value of
a) \( \displaystyle \cos (75^{\circ} ) \) b) \( \displaystyle \sec (15^{\circ} ) \)
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Find the exact value of
a) \( \displaystyle \tan (-330^{\circ} ) \) b) \( \displaystyle \csc (480^{\circ} ) \)
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Prove the idendity
a) \( \displaystyle \cot x + \sec x \sin x = 1+\tan x \)
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Find angle \( \theta \) in the range \( [0 , 360^{\circ} ) \) such that
a) \( \displaystyle \tan( \theta ) = 0.2\) b) \( \displaystyle \cos(\theta + 30^{\circ} ) = 0.5\)
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The water depth \( d \) (in meters) in a harbor at \( t \) hours after midnight is given by \( d(t) = 7.2 \cos ( 30^{\circ}(t - 6.5) ) + 5.8 \)
a) What is the maximum depth of water and when does it occur?
b) What is the minimum depth of water and when does it occur?
c) Sketch \( d \) as a function of \( t \) over two periods.
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Sketch the graph of \( y = - 2^{x-2} - 3 \)
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Sketch the graph of \( y = -3 \cos (x - 30^{\circ}) + 3\)
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Simplify the expression
\( \displaystyle \left( 2^{\frac{1}{5}} x^{\frac{1}{2}} \right) \left( 16^{\frac{1}{5}} x^{\frac{1}{2}} \right) \).
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Solve the equation
\( \displaystyle \frac{1}{8 ^x \; 4^x}\:= 2^{-7x+\frac{1}{2}} \).
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Find all values of \( m \) so that the equation in \( x \) given below has two real solutions.
\( \displaystyle 2x^2 - x + m = 1 \).
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Find the points of intersection of the graph of the following pair of equations.
\( \displaystyle (x - 2)^2 + (y + 1)^2 = 5 \) and \( \displaystyle 4x - 2 y = 4 \) .
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The third term of a geometric sequence is equal to \( -18 \) and the fourth term is equal to \( 54 \). Find the seventh term of the sequence and the sum of the first ten terms of the sequence.
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What amount must be invested in order to have \( \$20 000 \) in \( 10 \) years at the rate of \( 6\% \) compunded semi annually ?
More References and links
- More High School Math