Daily Practice · Higher Plus
August 1970 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1970 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1970
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1970A car covers 520 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 2nd August 1970Work out the nth term of the quadratic sequence 4, 9, 18, 31, ...
- 3rd August 1970A train slows steadily from 38 m/s to rest in 10 seconds. Work out its deceleration.
- 4th August 1970A cuboid measures 12 cm by 4 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th August 1970A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th August 1970A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 7th August 1970Rationalise the denominator of 60/sqrt(5), giving your answer in its simplest form.
- 8th August 1970The point (-3, -6) lies on y = f(x). Write down its image on y = f(x - 4).
- 9th August 1970y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 10th August 1970A cuboid measures 5 cm by 8 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th August 1970A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th August 1970On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th August 1970Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 14th August 1970Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 15th August 1970y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 16th August 1970The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 17th August 1970A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 18th August 1970A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 19th August 1970A rectangle is 29 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th August 1970f(x) = 2x - 6 and g(x) = 5x + 7. Work out fg(2).
- 21st August 1970y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 64.
- 22nd August 1970In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 23rd August 1970The probability of winning a game is 4/5. A player expects 96 wins. How many games did they play?
- 24th August 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?
- 25th August 1970Expand and simplify (6 + sqrt(5))(6 - sqrt(5)).
- 26th August 1970The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 27th August 1970A train slows steadily from 26 m/s to rest in 10 seconds. Work out its deceleration.
- 28th August 1970In a vector proof you find that vector PQ = 6a + 2b and vector RS = 18a + 6b. What does this show about PQ and RS?
- 29th August 1970A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 30th August 1970A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 31st August 1970A block has mass 570 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.