#### Description

Test your knowledge on Algebraic Equations level 3

##### Study Set Content:
1- Question

In the quadratic 2(x^2) - 7x - 7 = 0, what are the values of a, b and c?

a = 2, b = 7 and c = 7
a = -2, b = -7 and c = -7
a = 2, b = -7 and c = -7
2- Question

Solve 2(x^2) - 7x - 7 = 0, leaving the answer in surd (square root) form.

(7 ± suq(105) ) / 4
(-7 ± suq(105) ) / 4
(7 ± suq(105) ) / 2
3- Flashcard What is the equation simplified?

To simplify rational expressions such as this, look for common factors. There is a common factor of 2k. Dividing by this throughout gives 2k.

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4- Flashcard What is the equation simplified?

There is a common factor of (j + 2) throughout the fraction.

Cancelling this gives 3(j + 2).

As there is no common factor of 3, the 3 remains in the numerator and is not cancelled out.

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5- Flashcard What is the equation simplified?

The common factor of (y + 3) is cancelled out.

The fraction simplifies to (y−6)/5.

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6- Flashcard What is the equation simplified?

The numerator of the fraction can be factorised to 4(p - 1).

A common factor of 4 can now be seen, which simplifies

the fraction to p - 1.

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7- Flashcard What is the equation simplified? If the denominator of two fractions is the same, they can be added simply by adding the numerators. .

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8- Flashcard What is the equation simplified? To add or subtract fractions, there must be a common denominator.

The lowest common multiple of 5a and 3a is 15a.

This gives (18/15a)−(5/15a)

This gives

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9- Flashcard What is the equation expressed as a single fraction? To add or subtract fractions, there must be a common denominator. To get a common denominator, the denominators must be multiplied together.

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10- Flashcard What is the result of multiplying To multiply fractions, multiply the numerators and multiply the denominators.

Either simplify BEFORE or AFTER the multiplication, if possible.

after cancelling the common factors of 6w.

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11- Flashcard What is the final result of dividing To divide two fractions, keep the first fraction the same, turn the divide sign to a multiply and flip the second fraction upside down.

Then multiply the two fractions together. This is known as multiplying by the reciprocal.

This cannot be simplified as there are no common factors.

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12- Question

Which of the following is an example of an expression?

2a + 4 = 6
3a × a = 3(a^2)
4ab + 3b - 7c
13- Question

Lee buys h packs of hotdogs and b packs of buns for a party. Hotdogs come in packs of 8 and buns come in packs of 12. Write an expression for the total number of hotdogs and buns bought, in terms of h and b.

12h + 8b
8h + 12b
96bh
14- Question

How can you simplify 4e × 2ef?

8(e^2)f
8e(f^2)
(8ef)^2
15- Question

Simplify the following expression: 3(s^2) + 6s - (s^2) - 8s.

18(s^2)
2(s^2) - 2s
16- Question

How can you simplify 24a(b^2) ÷ 6b?

4
4ab
4b
17- Question

Expand the bracket 4(2m - 7).

8m – 28
6m – 11
6m - 7
18- Question

Expand and simplify 5 + 2(3a + 7).

21a + 49
21a + 7
6a + 19
19- Question

Factorise 4(x^2) - 14xy fully.

x(4x - 14y)
2x(2x - 7y)
2(2(x^2) - 7xy)
20- Flashcard

Simplify 9c−7d+c+3d+5.

This expression contains three types of terms: the terms that contain c's, terms that contain d's and terms that are numbers alone.

To simplify this expression, collect the like terms.

9c−7d+c+3d+5

9c+c=10c

−7d+3d=−4d

+5

This gives 10c−4d+5.

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