Daily Practice · Higher Plus
February 2005 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2005, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2005 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2005A cuboid measures 15 cm by 5 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd February 2005A 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?
- 3rd February 2005A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 4th February 2005Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
- 5th February 2005In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 6th February 2005y is inversely proportional to x^2. When x = 5, y = 27. Work out y when x = 3.
- 7th February 2005A cuboid measures 14 cm by 12 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th February 2005A bag holds 3 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th February 2005On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th February 2005Simplify sqrt(32) + sqrt(18), giving your answer in the form a sqrt(b).
- 11th February 2005Make x the subject of 4x + 7 = y(x + 7).
- 12th February 2005y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 13th February 2005The 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.
- 14th February 2005A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 15th February 2005A 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?
- 16th February 2005A rectangle is 19 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th February 2005Write 5/(x - 4) + 6/(x + 4) as a single fraction.
- 18th February 2005y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 9.
- 19th February 2005In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 20th February 2005The probability of winning a game is 1/4. A player expects 6 wins. How many games did they play?
- 21st February 2005On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd February 2005Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
- 23rd February 2005Solve 10x^2 + 29x + 10 = 0.
- 24th February 2005A train slows steadily from 18 m/s to rest in 4 seconds. Work out its deceleration.
- 25th February 2005In a vector proof you find that vector PQ = 6a - 3b and vector RS = 24a - 12b. What does this show about PQ and RS?
- 26th February 2005A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 27th February 2005A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 28th February 2005A block has mass 720 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.