Daily Practice · Higher Plus
October 1961 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1961 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1961
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1961y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 2nd October 1961The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 3rd October 1961A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 4th October 1961A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 5th October 1961Simplify sqrt(20) + sqrt(125), giving your answer in the form a sqrt(b).
- 6th October 1961Write x^2 + 8x - 10 in the form (x + a)^2 + b.
- 7th October 1961y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 64.
- 8th October 1961In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 9th October 1961The probability of winning a game is 1/10. A player expects 2 wins. How many games did they play?
- 10th October 1961On 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?
- 11th October 1961A rectangle is 16 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th October 1961Work out the coordinates of the turning point of y = x^2 - 4x - 1.
- 13th October 1961A train slows steadily from 22 m/s to rest in 4 seconds. Work out its deceleration.
- 14th October 1961In a vector proof you find that vector PQ = a + b and vector RS = 4a + 4b. What does this show about PQ and RS?
- 15th October 1961A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 16th October 1961A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 17th October 1961Expand and simplify (5 + sqrt(2))(5 - sqrt(2)).
- 18th October 1961Simplify (x^2 - 4x + 3)/(x - 3).
- 19th October 1961y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 20th October 1961A cuboid measures 10 cm by 11 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st October 1961A bag holds 6 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd October 1961On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 23rd October 1961A block has mass 290 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th October 1961In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 25th October 1961y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 26th October 1961A cuboid measures 13 cm by 14 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th October 1961A bag holds 3 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th October 1961A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 29th October 1961x = 84 and y = 69, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th October 1961Make x the subject of 8x + 7 = y(x + 7).
- 31st October 1961y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 16.