Pre-IB Math Formative
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Name………………………………………
1.
A hemisphere is cut out of a gold cuboid of dimensions 5cm, 3cm, 2cm. Find 𝑟, the
radius of the hemisphere, such that the gold wasted is only 20% of the total cuboid
volume.
2.
Rearrange to make 𝑥 the subject:
3𝑥 + 2
=𝑦
𝑥−2
3.
Fully simplify the following:
3𝑥 ! + 7𝑥 − 6
𝑥 ! + 3𝑥
4.
Fully factorise the following:
5.
Find the coordinates when the curve 𝑦 = 4𝑥 ! + 6𝑥 + 3 intersects with the line
𝑦 = −2𝑥 + 5
5.
Simplify fully:
200𝑥 ! − 50𝑦 "
!
/100𝑦𝑥 " × √27𝑥 !
(2𝑥𝑦)#
6.
Solve:
7
1
+
=4
𝑥+2 𝑥−1
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7.
In the following triangle 𝐴𝐶 = 𝑥 + 7, 𝐶𝐵 = 𝑥, 𝐴𝐵 = 2𝑥 + 3. Find 𝑥 :
8.
(i)
Write the quadratic 𝑦 = 3𝑥 ! + 12𝑥 − 2 in the form 𝑦 = 𝑎(𝑥 + 𝑝)! − 𝑞
(ii)
Write down the coordinates of the vertex of the graph.
9.
Terry writes down five numbers. The mean of his first three numbers is −3. The mean
of his first four numbers is 4. The mean of his first five numbers is −5. What is the
difference between his fourth number and his fifth number?
10.
The product of two positive integers is equal to twice their sum. This product is also
equal to six times the difference between the two integers. What is the sum of these
two integers?
11.
PQRS is a square. Point T lies on PQ so that PT ∶ TQ = 1: 2. Point U lies on SR so that
SU ∶ UR = 1: 2. The perimeter of PTUS is 40cm. What is the area of PTUS?
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