Daily Practice · Higher Plus
October 1969 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1969 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1969
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1969y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 2nd October 1969In a vector proof you find that vector PQ = 5a + 4b and vector RS = 15a + 12b. What does this show about PQ and RS?
- 3rd October 1969A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 4th October 1969On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th October 1969x = 71 and y = 53, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th October 1969The point (-2, 1) lies on y = f(x). Write down its image on y = f(-x).
- 7th October 1969y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 8th October 1969A cuboid measures 9 cm by 3 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th October 1969A 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?
- 10th October 1969A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 1.4. How many values in total?
- 11th October 1969A car covers 160 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th October 1969Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 13th October 1969y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 64.
- 14th October 1969A cuboid measures 11 cm by 5 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th October 1969A bag holds 5 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th October 1969On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 17th October 1969Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
- 18th October 1969f(x) = 2x - 1 and g(x) = 2x + 6. Work out fg(6).
- 19th October 1969A train slows steadily from 13 m/s to rest in 8 seconds. Work out its deceleration.
- 20th October 1969The 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.
- 21st October 1969A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 22nd October 1969A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 23rd October 1969Simplify sqrt(80) + sqrt(5), giving your answer in the form a sqrt(b).
- 24th October 1969The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 25th October 1969y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 26th October 1969In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 27th October 1969The probability of winning a game is 5/8. A player expects 20 wins. How many games did they play?
- 28th October 1969On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 29th October 1969A rectangle is 5 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th October 1969A quadratic sequence starts 13, 27, 51, 85. Work out the second difference, and the coefficient of n^2.
- 31st October 1969y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.