Daily Practice · Higher Plus
October 1974 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1974 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1974
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1974The probability of winning a game is 1/4. A player expects 4 wins. How many games did they play?
- 2nd October 1974On 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 October 1974Simplify sqrt(20) + sqrt(5), giving your answer in the form a sqrt(b).
- 4th October 1974Use the iteration x(n+1) = cube root of (4x(n) + 9) with x(0) = 3. Work out x(1) to 3 decimal places.
- 5th October 1974y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 6th October 1974In a vector proof you find that vector PQ = 5a + 2b and vector RS = 10a + 4b. What does this show about PQ and RS?
- 7th October 1974A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 8th October 1974A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 9th October 1974A rectangle is 13 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th October 1974Work out the nth term of the quadratic sequence 5, 9, 15, 23, ...
- 11th October 1974y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 64.
- 12th October 1974A cuboid measures 15 cm by 5 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th October 1974A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th October 1974On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th October 1974Expand and simplify (9 + sqrt(11))(9 - sqrt(11)).
- 16th October 1974The point (3, -4) lies on y = f(x). Write down its image on y = f(x - 4).
- 17th October 1974A train slows steadily from 34 m/s to rest in 4 seconds. Work out its deceleration.
- 18th October 1974A cuboid measures 13 cm by 13 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th October 1974A bag holds 3 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th October 1974A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 21st October 1974A block has mass 840 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd October 1974Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 23rd October 1974y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 24th October 1974The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 25th October 1974A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 26th October 1974On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 27th October 1974x = 106 and y = 35, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th October 1974f(x) = 2x - 5 and g(x) = 3x + 9. Work out fg(3).
- 29th October 1974y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 30th October 1974In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 31st October 1974The probability of winning a game is 1/2. A player expects 40 wins. How many games did they play?