Daily Practice · Higher Plus
October 1963 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1963 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1963
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1963Expand and simplify (7 + sqrt(6))(7 - sqrt(6)).
- 2nd October 1963Simplify (x^2 - 2x - 48)/(x - 8).
- 3rd October 1963A train slows steadily from 36 m/s to rest in 10 seconds. Work out its deceleration.
- 4th October 1963In a vector proof you find that vector PQ = a + 5b and vector RS = 4a + 20b. What does this show about PQ and RS?
- 5th October 1963A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 6th October 1963A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 7th October 1963A block has mass 430 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th October 1963In an algebraic proof, how would you write an even number in terms of an integer n?
- 9th October 1963y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 10th October 1963A cuboid measures 11 cm by 13 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th October 1963A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th October 1963On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th October 1963x = 150 and y = 34, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th October 1963Make x the subject of 3x + 6 = y(x + 6).
- 15th October 1963y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 16th October 1963A cuboid measures 6 cm by 8 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th October 1963A bag holds 3 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th October 1963A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 19th October 1963A car covers 290 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 20th October 1963Write 5/(x - 1) + 7/(x - 2) as a single fraction.
- 21st October 1963y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 64.
- 22nd October 1963The 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.
- 23rd October 1963A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 24th October 1963On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 25th October 1963Rationalise the denominator of 55/sqrt(5), giving your answer in its simplest form.
- 26th October 1963Solve 9x^2 - 21x + 10 = 0.
- 27th October 1963A train slows steadily from 33 m/s to rest in 4 seconds. Work out its deceleration.
- 28th October 1963In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 29th October 1963The probability of winning a game is 3/5. A player expects 45 wins. How many games did they play?
- 30th October 1963A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 31st October 1963Simplify sqrt(8) + sqrt(18), giving your answer in the form a sqrt(b).