Practice Test Geeks(BECE) Basic Education Certificate Examination Practice Test
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Algebraic Expressions and Equations Flashcards

6 cards from real BECE practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 Algebraic Expressions and Equations flashcards as text

  1. Simplify the expression: 5(x + 2y) - 3(2x - y)

    Answer: 13y - x

    First, distribute the numbers outside the brackets to the terms inside. 5 * x = 5x, and 5 * 2y = 10y. So the first part is 5x + 10y. For the second part, -3 * 2x = -6x, and -3 * -y = +3y. So the second part is -6x + 3y. Now combine the two parts: (5x + 10y) + (-6x + 3y). Group like terms: (5x - 6x) + (10y + 3y). This simplifies to -x + 13y, which is the same as 13y - x.

  2. Ama is twice as old as her brother Kofi. In 5 years, the sum of their ages will be 28. How old is Kofi now?

    Answer: 6 years

    Let Kofi's current age be 'k'. Then Ama's current age is '2k'. In 5 years, Kofi's age will be k+5 and Ama's age will be 2k+5. The sum of their ages in 5 years will be (k+5) + (2k+5) = 28. Combine like terms: 3k + 10 = 28. Subtract 10 from both sides: 3k = 18. Divide by 3: k = 6. Therefore, Kofi is currently 6 years old.

  3. If 4(x - 3) = 2x + 6, what is the value of x?

    Answer: 9

    To solve for x, first distribute the 4 on the left side of the equation: 4x - 12 = 2x + 6. Next, gather the x terms on one side by subtracting 2x from both sides: 2x - 12 = 6. Then, gather the constant terms on the other side by adding 12 to both sides: 2x = 18. Finally, divide by 2 to find x: x = 9.

  4. Which of the following expressions is equivalent to 3x² + 9x?

    Answer: 3x(x + 3)

    To find the equivalent expression, we need to factorize 3x² + 9x. The greatest common factor (GCF) of 3x² and 9x is 3x. When we factor out 3x, we divide each term by 3x. 3x² / 3x = x, and 9x / 3x = 3. Therefore, the factored form is 3x(x + 3).

  5. A rectangle has a length that is 5 cm more than its width. If the perimeter of the rectangle is 38 cm, what is its width?

    Answer: 7 cm

    Let the width be 'w'. The length is 'w + 5'. The formula for the perimeter of a rectangle is P = 2(length + width). So, 38 = 2((w + 5) + w). Simplify inside the bracket: 38 = 2(2w + 5). Distribute the 2: 38 = 4w + 10. Subtract 10 from both sides: 28 = 4w. Divide by 4 to find the width: w = 7 cm.

  6. Solve the equation: (2y/3) - 1 = 5

    Answer: y = 9

    First, isolate the term with the variable 'y'. Add 1 to both sides of the equation: 2y/3 = 5 + 1, which simplifies to 2y/3 = 6. To solve for y, multiply both sides by 3: 2y = 6 * 3, so 2y = 18. Finally, divide both sides by 2: y = 9.