Daily Practice · Higher Plus
January 1970 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1970 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1970
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1970A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 2nd January 1970A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 3rd January 1970A car covers 560 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th January 1970Use the iteration x(n+1) = cube root of (4x(n) + 9) with x(0) = 3. Work out x(1) to 3 decimal places.
- 5th January 1970y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 6th January 1970A cuboid measures 13 cm by 10 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th January 1970A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th January 1970On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th January 1970Rationalise the denominator of 18/sqrt(6), giving your answer in its simplest form.
- 10th January 1970Work out the nth term of the quadratic sequence 5, 15, 29, 47, ...
- 11th January 1970y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 12th January 1970A cuboid measures 10 cm by 5 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th January 1970A bag holds 3 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th January 1970A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 15th January 1970Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
- 16th January 1970The point (-5, -5) lies on y = f(x). Write down its image on y = -f(x).
- 17th January 1970y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 9.
- 18th January 1970The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 19th January 1970A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 20th January 1970On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st January 1970A rectangle is 11 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd January 1970Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 23rd January 1970A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 24th January 1970In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 25th January 1970The probability of winning a game is 1/5. A player expects 2 wins. How many games did they play?
- 26th January 1970A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 27th January 1970Expand and simplify (2 + sqrt(2))(2 - sqrt(2)).
- 28th January 1970f(x) = 6x - 9 and g(x) = 2x - 7. Work out fg(0).
- 29th January 1970y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 30th January 1970In a vector proof you find that vector PQ = 3a + 4b and vector RS = 15a + 20b. What does this show about PQ and RS?
- 31st January 1970A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.