Daily Practice · Higher Plus
October 1958 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1958 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1958
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1958A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 2nd October 1958On 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?
- 3rd October 1958Rationalise the denominator of 12/sqrt(3), giving your answer in its simplest form.
- 4th October 1958Make x the subject of 2x + 2 = y(x + 2).
- 5th October 1958A train slows steadily from 18 m/s to rest in 5 seconds. Work out its deceleration.
- 6th October 1958A cuboid measures 13 cm by 5 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th October 1958A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th October 1958A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 9th October 1958Simplify sqrt(75) + sqrt(12), giving your answer in the form a sqrt(b).
- 10th October 1958Write 2/(x + 6) + 3/(x - 1) as a single fraction.
- 11th October 1958y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 12th October 1958A cuboid measures 7 cm by 6 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th October 1958A bag holds 3 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th October 1958On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 15th October 1958A rectangle is 18 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th October 1958Solve 20x^2 - x - 12 = 0.
- 17th October 1958y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 18th October 1958The 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.
- 19th October 1958A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 20th October 1958A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 21st October 1958Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 22nd October 1958f(x) = 8x + 8. Work out the inverse function f^-1(x).
- 23rd October 1958y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 81.
- 24th October 1958In 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 October 1958The probability of winning a game is 1/4. A player expects 8 wins. How many games did they play?
- 26th October 1958On 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?
- 27th October 1958A block has mass 360 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th October 1958Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 29th October 1958A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 30th October 1958In a vector proof you find that vector PQ = 3a + 3b and vector RS = 15a + 15b. What does this show about PQ and RS?
- 31st October 1958A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.