NCUK SEMESTER I EXAM (17/18 V1) B1, B2, B3

Solve the inequality  $\frac{8x+5}{4}\le-7$  

•  $x\le-\frac{33}{8}$  

•  $x\le-\frac{21}{5}$  

•  $x\le-\frac{41}{7}$  

•  $x\le-\frac{52}{11}$  

Solve the inequality  $x^2+6x<0$  

•  $-6<x<6$  

•  $-6<x<0$  

•  $x<-6\ or\ x>0$  

•  $x<-6\ or\ x>6$  

The solution of  $\frac{8x+5}{4}\le-7$  is  $x\le-\frac{33}{8}$  .
The solution of  $x^2+6x<0$  is  $-6<x<0$  .
State the integer that satisfies both  $\frac{8x+5}{4}\le-7$  and  $x^2+6x<0$  .

• 5

• -6

• -4

• -5

The function  $f\left(x\right)$  is defined as  $f\left(x\right)=2x^3+7x^2-10x-24$  . Use the Remainder Theorem to find the reminder when  $f\left(x\right)$  is divided by  $\left(x+2\right)$  .

• -2

• 2

• 8

• 5

The function  $f\left(x\right)$  is defined as  $f\left(x\right)=2x^3+7x^2-10x-24$  . Divide  $f\left(x\right)$  by  $\left(x+4\right)$  .

•  $x^2-2x+7$  

•  $2x^2-x-6$  

•  $-x^2-4x+1$  

•  $2x^2+5x-1$  

The function  $f\left(x\right)$  is defined as  $f\left(x\right)=2x^3+7x^2-10x-24$  . The result of division of  $f\left(x\right)$  by  $\left(x+4\right)$  is  $2x^2-x-6$  . Factorise  $f\left(x\right)$  completely.

•  $\left(x+4\right)\left(2x+3\right)\left(x-2\right)$  

•  $\left(x+5\right)\left(2x+1\right)\left(x-7\right)$  

•  $\left(x+4\right)\left(2x-3\right)\left(x+2\right)$  

•  $\left(x-4\right)\left(x+3\right)\left(x-2\right)$  

Point P lies at (11 - a, a - 7). Point Q lies at (a - 1, 2a - 3). The gradient of line PQ is 3. Find the value of a.

• 5

• 4

• 8

• 7

A box holds 3 red beads and 2 blue beads. Two beads are drawn, one after the other and with no replacement. Draw and label a tree diagram.

• 
• 

A box holds 3 red beads and 2 blue beads. Two beads are drawn, one after the other and with no replacement (see the tree diagram above). Find the probability that both beads will be of the same colour.

• 0.4

• 0.3

• 0.1

• 0.6

Figure 1 shows the acute angled triangle ABC with AB = 18.5 cm, AC = 22 cm and angle A = θ. The area of triangle ABC is 66 cm².

Find the value of sinθ, giving your answer in the form m/n where m and n are integers. All working must be shown.

• 15/41

• 12/37

• 13/42

• 11/50