Let Q=$\frac{(sin2x+b)(2sinx-1)}{a^2-4tanx}$,where x =45${}^{\circ }$. a=18 and b =$\sqrt{2}$.
1.Find the exact value of Q.
Q=  .
2.Give your answer to part (a) correct to

2.1.three decimal places;
The number is   .
2.2.three significant figures.
The number is   .
3.Calculate the percentage error if Q is given to three decimal places.
Using the percentage error formula ϵ=  %

  The distance between two points with coordinate3+fz i4w.edcg0 j ga,ds (x${}_1$,y${}_1$) and (x${}_2$,y${}_2$) is equal to
$\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.
1.Calculate the distance between points A(40,−100) and B(1,−2). Give your answer correct to three significant figures.
The distance between points A(40,−100) and B(1,−2) is AB≈  .
2.Give your answer from part (a) correct to one decimal place.The number=  .

3.Write the answer to part (b) in the form a×10${}^k$, where 1≤a<10, k∈Z.The number=  ×104${}^2$

  Let F=$\frac{(4sin2z-1)(2tan3z+1)}{x^2-y^2}$,where x=12, y=8 and z=15°.

1.Calculate the exact value of F.
F=  .
2.Give your answer to F correct to

2.1.two significant figures;The number=  .

2.2.two decimal places.The number=  .

Sasha estimates the value of F to be 0.03.

3.Calculate the percentage error in Sasha's estimate.the percentage=  %.

  
1.Find the value of A. Write down your full calculator display.
A=  .
2.Give your answer to part (a) correct to

2.1.three significant figures;
The number=  .
2.2.three decimal places.
The number=  .
3.Give the answer to part (b) (i) in the form a×10${}^k$, where 1≤a<10, k∈Z.
The number=  ×10${}^{-2}$.

  A cuboid has the following dimensions: length=9.6 cm, width/g4 * vl *nw.pwr9cive=7.4 cm, and height=5.2 cm. r.*pwn94g* wvvc ei/l

1.Calculate the exact value of the volume of the cuboid, in cm${}^3$
V=  cm${}^3$.
2.Write your answer to part (a) correct to

2.1.two decimal places;
The number=  .
2.2.three significant figures.
The number=  .
3.Write your answer to part (b) (ii) in the form a×10${}^k$ , where 1≤a<10 and k∈Z.The number=  ×10${}^2$.

  Four cement bags labelled, "5 kg", were delivered to a custof,mkhh,u 1lz1 ysi9h kwd:m+0 mer. The customer measured each bag to check their weights and recorded the following90,l:+iumh,w k fhhkz sm1d1y :

4.92,4.95,5.02,4.95
​
1.1.Find the mean of the customer's measurements.
If we calculate the mean of the measurements, we get μ=  .
1.2.Calculate the percentage error between the mean and the stated,
approximate weight of 5 kg.
Using the percentage error formula ϵ=  %.

2.1.correct to the nearest integer;
The number=  .
2.2.in the form a×10${}^k$, where 1≤a<10 and k∈Z.
The number=  ×10${}^1$.

  After solving a problem, John has an exact answer zg1w l:r33xhlk cyl80of z=0.1475.

1.Write down the exact value of z in the form a×10${}^k$ , where 1≤a<10,k∈Z.
The number=  ×10${}^{-1}$.
2.State the value of z given correct to 2 significant figures.
The number=  .
3.Calculate the percentage error if z is given correct to 2 significant figures.
Using the percentage error formula ϵ=  %.

  Given that z=$\frac{10sina}{3x+y}$,where α=30°, x=6 and y=46.
1.Find the exact value of z. z=  .

2.Write your answer to part (a)

2.1.correct to 2 decimal places;
The number=  .
2.2.correct to 3 significant figures;
The number=  .
2.3.in the form a×10${}^k$ , where 1≤a<10 and k∈Z.
The number=  ×10${}^{-2}$.

  The following diagram s; n1 x1hlicx3r4 lgj4mhows a rectangle with sides of length 7.6×10${}^2$cm and 1.5×10${}^3$cm.

1.Write down the area of the rectangle in the form a×10${}^k$ , where1≤a<10 and k∈Z.

Natalie estimates the area of the rectangle to be 1200000 cm.
A=  ×10${}^6$

2.Find the percentage error in Natalie's estimate.
Using the percentage error formula ϵ=  %

  The volume of a hemisphere, V, is given by tht.b;k p wa1sp)e formula

where S is the total surface area.

The total surface area of a given hemisphere is 529 cm${}^2$.

1.Calculate the volume of this hemisphere in cm${}^3$ . Give your answer correct to one decimal place.
V=  cm${}^3$
2.Write down your answer to part (a) correct to the nearest integer.
The number=  cm${}^3$.
3.Write down your answer to part (b) in the form a×10${}^k$ , where 1≤a<10 and k∈Z.
The number=  ×10${}^2$ cm${}^3$.

  
1.calculate the value of r.
r=  .
Albert first writes a, b and c correct to one significant figure and then uses these values to estimate the value of r.

2.1.Write down a, b and c each correct to one significant figure.
a=  ,b=  ,c=  .
2.2.Find Albert's estimate of the value of r.
r=  .
3.Calculate the percentage error in Albert's estimate of the value of r.
Using the percentage error formula ϵ=  %.