Worksheet: Evaluating Simple and Rational Algebraic Expressions

In this worksheet, we will practice evaluating simple and rational algebraic expressions with one or two variables by direct substitution at specific values.

Q1:

Given that the area of a trapezium is 𝐴 = 1 2 β„Ž ( π‘Ž + 𝑏 ) , find the value of 𝐴 when β„Ž = 4 c m , π‘Ž = 3 2 c m , and 𝑏 = 5 2 c m .

Q2:

Starting from his school, Bassem cycled 10 miles, stopped at his friend’s house, and later continued cycling in the same direction as before. The equation shows the relationship between the number of miles he cycled after leaving his friend’s house and the distance he was from his school. If he ended up 32 miles from his school, how far is he from his friends house?

Q3:

The total surface area, 𝑇 , of a cuboid is given by 𝑇 = 2 ( π‘₯ 𝑦 + 𝑦 𝑧 + 𝑧 π‘₯ ) . Find the value of 𝑇 when π‘₯ = 5 , 𝑦 = 1 , and 𝑧 = 9 .

Q4:

Use the formula 𝐴 = 𝑏 β„Ž to find the area of a parallelogram whose base, 𝑏 , is 2 1 2 and height, β„Ž , is 4 5 .

  • A 1 2 7
  • B 2 2 5
  • C 3 1 8
  • D2
  • E 1 2 3

Q5:

What is the volume of a cube of edge length 5 π‘₯ cm?

  • A 1 5 π‘₯ cm3
  • B 2 5 π‘₯ 2 cm3
  • C 1 2 5 π‘₯ cm3
  • D 1 2 5 π‘₯ 3 cm3

Q6:

If a rectangle has a length of 13 centimetres and a width of 12 centimetres, determine, in the simplest form, what fraction of the perimeter the width is.

  • A
  • B
  • C
  • D
  • E

Q7:

One measure of distance is rate multiplied by time, . Find the distance Dalia travels if she is moving at a rate of 60 mph for 6.75 h.

Q8:

Samar was given a $50 bill to buy 2 yogurt cups, each for dollars. She had remaining. Calculate the amount remaining if each yogurt cup cost $3.

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