Correct answer: (4x + 3)². 16x² + 24x + 9 = (4x)² + 2(4x)(3) + 3² = (4x + 3)².
Background: It is a perfect square trinomial of the form a² + 2ab + b².
Did you know? The middle term 24x = 2 × 4x × 3 matches.
Memory trick: a² + 2ab + b² = (a + b)².
Correct answer: 5, −2. Factorising gives (x − 5)(x + 2) = 0, so x = 5 or x = −2.
Background: Find two numbers with product −10 and sum −3: that is −5 and +2.
Did you know? Check: 25 − 15 − 10 = 0.
Memory trick: Product −10, sum −3.
Correct answer: 39999. 201 × 199 = (200 + 1)(200 − 1) = 200² − 1 = 40000 − 1 = 39999.
Background: Use the identity (a + 1)(a − 1) = a² − 1.
Did you know? It is quicker than long multiplication.
Memory trick: 200² − 1².
Correct answer: 5 m. tan 45° = 1 = 5 ÷ height, so height = 5 m.
Background: At 45°, the triangle is isosceles, so base = height.
Did you know? tan 45° = 1.
Memory trick: 45° → equal sides.
Correct answer: 50. By the remainder theorem, put x = −1: (−1)⁵¹ + 51 = −1 + 51 = 50.
Background: To divide by (x − a), put x = a.
Did you know? (−1) raised to an odd power is −1.
Memory trick: Put x = −1.
Correct answer: 49. Sugar 35 = 5 × 7, so water = 7 × 7 = 49.
Background: Multiply both parts of the ratio by the same number.
Did you know? The multiplier is 35 ÷ 5 = 7.
Memory trick: Same multiplier on both parts.
Correct answer: 5, 12, 19, 26. Adding 7 each time gives 5, 12, 19, 26.
Background: In an A.P., each term is the previous term plus the common difference.
Did you know? The terms are a, a + d, a + 2d, a + 3d.
Memory trick: Keep adding 7.
Correct answer: 224. In a proportion, 7 × x = 8 × 196, so x = 1568 ÷ 7 = 224.
Background: In a : b :: c : d, we have a × d = b × c.
Did you know? 196 ÷ 7 = 28, and 8 × 28 = 224.
Memory trick: Cross-multiply.
Correct answer: Both A & B. Hydrophytes (water plants) have little mechanical tissue and have aerenchyma (air spaces) to float.
Background: Hydrophytes grow in or on water.
Did you know? Examples are water lily and Hydrilla.
Memory trick: Water plants: soft + air spaces.
Correct answer: 31. The differences are 6, 8, 10, 12, 14, so the missing term is 21 + 10 = 31.
Background: If the pattern is not clear, find the differences between terms.
Did you know? Check: 31 + 12 = 43 and 43 + 14 = 57.
Memory trick: Differences go up by 2.
Correct answer: 100√3 cm². Side = 60 ÷ 3 = 20 cm, and area = (√3/4) × 20² = 100√3 cm².
Background: The area of an equilateral triangle is (√3/4) × side².
Did you know? Perimeter = 3 × side.
Memory trick: Area = (√3/4) a².
Correct answer: 49 m². The side is ∛343 = 7 m, so the area of one face = 7² = 49 m².
Background: Volume of a cube = side³.
Did you know? 7 × 7 × 7 = 343.
Memory trick: Cube root, then square.
Correct answer: 64. The pattern alternates ×2 and +3: 2, 4, 7, 14, 17, 34, 37, 74. The last term should be 74, so 64 is incorrect.
Background: Look for alternate operations when the pattern is not simple.
Did you know? 37 × 2 = 74.
Memory trick: ×2, +3, ×2, +3 …
Correct answer: SMTP & POP. SMTP is used to send e-mail and POP is used to receive it.
Background: IMAP is another protocol for receiving e-mail.
Did you know? SMTP stands for Simple Mail Transfer Protocol.
Memory trick: SMTP sends; POP picks up.
Correct answer: Slide Show view. Slide Show view displays the slides full screen, without the menus and other elements.
Background: You can start it by pressing F5.
Did you know? Press Esc to leave Slide Show view.
Memory trick: Slide Show = full screen, no tools.
Correct answer: All of these. A Turing machine is a model of computation that is used in the theory of problem solving and is a foundation for ideas in AI.
Background: Alan Turing described it in 1936.
Did you know? A Turing machine reads and writes symbols on an endless tape.
Memory trick: Turing machine = model of computing.
Correct answer: Reduce file size. Data compression reduces the size of a file so it takes less space and sends faster.
Background: ZIP is a common compression format.
Did you know? JPEG and MP3 use lossy compression.
Memory trick: Compress = make smaller.
Correct answer: Limiting networking accessibility. Cloud computing offers broad network access, so limiting network accessibility is not a characteristic.
Background: Cloud services are available over the network.
Did you know? Cloud also uses “measured service”, so you pay for what you use.
Memory trick: Cloud = open access, not limited.
Correct answer: Regression Test. Regression testing checks that new changes have not broken existing features.
Background: Regression tests are rerun after every update.
Did you know? “Regression” means going back to check old features.
Memory trick: Regression = check old still works.
Correct answer: SpaceX & Tesla. Elon Musk is the CEO of SpaceX and Tesla.
Background: He also owns the social media platform X.
Did you know? SpaceX builds rockets and Tesla builds electric cars.
Memory trick: Musk = SpaceX + Tesla.
Correct answer: DHCP. DHCP (Dynamic Host Configuration Protocol) automatically gives IP addresses to devices.
Background: A router usually acts as the DHCP server at home.
Did you know? Without DHCP, IP addresses would have to be set manually.
Memory trick: DHCP = Dynamic IP.
Correct answer: Record. A row in a database table is called a record.
Background: Each record holds all the information about one item.
Did you know? A table is made up of records (rows) and fields (columns).
Memory trick: Row = Record; Column = Field.
Correct answer: WWW. Tim Berners-Lee invented the World Wide Web (WWW) in 1989–91.
Background: He worked at CERN in Switzerland.
Did you know? The Web is not the same as the internet.
Memory trick: WWW = Berners-Lee.
Correct answer: Local only access. Cloud computing offers access over networks, not local-only access.
Background: The main cloud characteristics are on-demand self-service, broad network access, resource pooling, rapid elasticity, and measured service.
Did you know? Cloud services can be reached from anywhere with an internet connection.
Memory trick: Cloud = reach from anywhere.
Correct answer: Speech recognition. Speech recognition converts spoken words into text or commands.
Background: Voice assistants use speech recognition.
Did you know? Examples are Siri, Google Assistant, and Alexa.
Memory trick: Speech = speech recognition.