Questions on how to evaluate algebraic expressions in algebra are presented along with answers and feedback. Hints on how to solve these questions are also included.
Q1) If \( x =1 \) , then \( 2x = \)
A. \( 0.5 \)
B. \( 1 \)
C. \( -2 \)
D. \( 2 \)
E. \( - 1\)
Substitute \( x \) by \( 1 \) ( meaning replace \( x \) by \(1 \) ) in the expression \(2x \) which becomes \( 2 (1) \) and then evaluate it.
Evaluate the expression \( 2x - 3y\) for \( x = 2 \) and \( y = -3 \)
A. \(1 \)
B. \(-1 \)
C. \(-13 \)
D. \(-5 \)
E. \(13 \)
Substitute \( x \) by \(2 \) (its given value) and \( y\) by \( -3 \) (its given value) in the expression \( 2x - 3 y \) which becomes \( 2 ( 2 ) - 3 ( - 3 ) \) and then evaluate it.
Q3) If \( a = \dfrac{1}{3} \), then \( -6 a = \)
A. \(- 2 \)
B. \(2 \)
C. \(-0.5 \)
D. \(-18 \)
E. \(18 \)
Substitute (replace) \( a \) by \( \dfrac{1}{3} \) in the expression \( - 6 a \) which gives \( - 6(\dfrac{1}{3}) \) then simplify it.
Q4) If \( F = 2 x^2 \), then for \( x = -2 \), \( F = \)
A. \( - 8 \)
B. \( 8 \)
C. \( - 6 \)
D. \( 6 \)
E. \( - 2 \)
Substitute \( x \) by \( - 2 \) in the formula \( F = 2 x^2 \) which gives \( F = 2 ( - 2 )^2 \). Now remember that \( ( - 2 )^2 = ( - 2 ) ( - 2 ) = 4 \). Now simplify to find the final value of \( F \).
Q5) For \( x = -3 \) and \( y = 2 \), \( x^2 + y^3 = \)
A. \( 1 \)
B. \( - 1 \)
C. \( 17 \)
D. \( - 17\) >
E. \( 0 \)
Substitute \( x \) by \(- 3 \) and \(y \) by \(2 \) in the expression \(x^2 + y^3\) to obtain \(( - 3 )^2 + ( 2 )^3 \) . Now remember that \( ( - 3 )^2 = ( - 3 ) ( - 3 ) = 9 \) and \( ( 2 )^3 = ( 2 ) ( 2 ) ( 2 ) = 8 \) , then simplify to evaluate.
Q6) If \( b = - \dfrac{1}{2} \), then \( b^2 = \)
A. \( 4 \)
B. \( - \dfrac{1}{4} \)
C. \( - 1\)
D. \( 1 \)
E. \( \dfrac{1}{4} \)
Substitute \( b \) by \( -\dfrac{1}{2} \) in the expression \( b^2 \) which gives \( ( -\dfrac{1}{2})^2 \). Now remember that \( ( -\dfrac{1}{2})^2 = ( -\dfrac{1}{2} ) ( -\dfrac{1}{2} ) \) . Simplify.
Q7) Evaluate \( 2x^2 + 3 x - 5 \) for \( x = -2 \)
A. \( 3 \)
B. \( - 3\)
C. \( - 19 \)
D. \( 9 \)
E. \( - 9 \)
Substitute (replace) \( x \) by \( - 2 \) in the given expression which becomes \( 2 ( - 2 )^2 + 3 ( - 2 ) - 5 \) then simplify.
Q8) If \( a = - 2 \) and \( b = \dfrac{1}{3} \), then \( 2 a^2 + 9b^2 - 2 = \)
A. \( 7 \)
B. \( - 7 \)
C. \( - 9 \)
D. \( - 11 \)
E. \( 5 \)
Substitute \( a \) by \( - 2 \) and \( b \) by \( \dfrac{1}{3} \) in the given expression which becomes \( 2 ( - 2 )^2 + 9 ( \dfrac{1}{3} ) ^ 2 - 2 \) and simplify
Q9) Evaluate the expression \( 4 x y + y^2 + 2 x y \) for \( x = \dfrac{1}{2} \) and \( y = - 3 \)
A. \( - 5 \)
B. \( 5 \)
C. \( 0\)
D. \( - 1 \)
E. \( 1 \)
Substitute \( x \) by \( \dfrac{1}{2} \) and \( y \) by \( - 3 \) in the given expression which gives \( 4 ( \dfrac{1}{2} ) ( - 3 ) + ( - 3 )^2 + 2 ( \dfrac{1}{2} ) ( - 3 ) \) and simplify.
Q10) If \( a = 1.1 \) and \( b = - 2.1 \), then \( 3 a + 4 b - a b = \)
A. \( - 3.79 \)
B. \( 2.99 \)
C. \( 2.79 \)
D. \( - 2.79 \)
E. \( - 3.99\)
Substitute \( a \) by \( 1.1 \) and \( b \) by \( -2.1 \) in the expression \( 3 a + 4 b - ab \) and then simplify. Use a calculator if necessary.