Daily Practice · Higher Plus
April 1970 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1970 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1970
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1970A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 2nd April 1970On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 3rd April 1970Rationalise the denominator of 121/sqrt(11), giving your answer in its simplest form.
- 4th April 1970f(x) = 4x + 9. Work out the inverse function f^-1(x).
- 5th April 1970A train slows steadily from 37 m/s to rest in 5 seconds. Work out its deceleration.
- 6th April 1970A cuboid measures 5 cm by 3 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th April 1970A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th April 1970A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 9th April 1970Simplify sqrt(12) + sqrt(12), giving your answer in the form a sqrt(b).
- 10th April 1970Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 11th April 1970y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 12th April 1970A cuboid measures 7 cm by 8 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th April 1970A bag holds 3 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th April 1970On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 15th April 1970A rectangle is 6 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th April 1970Use the iteration x(n+1) = cube root of (4x(n) + 1) with x(0) = 5. Work out x(1) to 3 decimal places.
- 17th April 1970y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 18th April 1970The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 19th April 1970A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 20th April 1970A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 21st April 1970Expand and simplify (2 + sqrt(11))(2 - sqrt(11)).
- 22nd April 1970Work out the nth term of the quadratic sequence 12, 22, 38, 60, ...
- 23rd April 1970y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 81.
- 24th April 1970In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 25th April 1970The probability of winning a game is 3/4. A player expects 12 wins. How many games did they play?
- 26th April 1970On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 27th April 1970A block has mass 420 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th April 1970The point (0, 3) lies on y = f(x). Write down its image on y = f(x) - 5.
- 29th April 1970A train slows steadily from 23 m/s to rest in 8 seconds. Work out its deceleration.
- 30th April 1970In a vector proof you find that vector PQ = 3a + 2b and vector RS = 12a + 8b. What does this show about PQ and RS?